Remote monitoring and operation evaluation applications for industrial environments are modern and easy means of exploiting the provided resources of specific systems. Targeted micro hydropower plant functionalities  require the design of reliable and efficient devices or systems. The present work describes the design and implementation procedure of an Industrial Internet of Things (IIoT) system configured for a basic micro hydropower plant architecture and assuring simple means of customization for plant differences in structure and operation. The designed system features a set of commonly used functions specific to micro hydropower exploitation, providing maximum performance and efficiency. The use of data acquisition systems for monitoring and control of specific events is currently widespread in most industries, even for estimation of the degree of wear and the development of maintenance programs for specific devices and systems. Specific software applications for data acquisition systems allow for fast identification of untimely faults, as well as their repair. The basic principles of data acquisition implementation have been applied in various architectures and successfully adapted to the various particularities of the implementation environment . MedicinThe acquired data are gathered for further analysis by an intelligent processing unit such as a data concentrator or a server, in most cases, serially collecting the required information. Although a handy and stable means of local data transfer, an increasing number of situations require remote monitoring, control, and data acquisition, requiring additional communication support. Optical fiber has been proven a suitable a solution for systems implementing applications designed to meet certain industrial control standards .In modern remote communication design, the use of IoT systems is spreading due to their ease of operation, provided features, and versatility. Low-cost IoT alternatives are currently implemented in domains such as medicine , industrVarious approaches in IoT and IIoT implementations can be chosen for applications depending on the targeted performance and requirements. Narrow-band IoT monitoring systems can be used to implement an efficient microgrid power quality monitoring solution . Low-cosThe design of many problem-specific IoT applications implementing various and handy protocols can lead to an impasse regarding the communication in wireless sensor networks due to the lack of standard-based network activity. A wireless sensor network architecture was designed in  with theIIoT solutions have recently gained popularity in the electric power domain by adapting these technology features to various targeted applications. Hydropower facilities specific to micro power plants have an architecture assuring the most efficient use of water as a primary resource. In this regard, a water tank is set upstream to collect water from the surrounding area. Meanwhile, several micro hydropower plants are installed downstream . The control of both types of resources is managed by a single control point placed either within the facility or at the headquarters of the managing company. This organizing mode requires the use of remote-control applications, most often implemented on GSM support. Such applications are suitable for the management of either a single micro hydropower plant or for a whole hydropower facility.The proper functioning of a hydropower facility disposing of micro power plants and lacking remote-control features implies either the existence of an operator for each component micro hydropower plant or a single operator periodically inspecting all the micro power plants. Both of these approaches lead to cost disadvantages (operator payment and inspection trip costs) and micro hydropower chain malfunctioning, as fault events cannot be rapidly removed (leading to machinery blockage or water discharges). As a consequence, real-time monitoring of parameters for each micro hydropower plant, signaling of faults, and their rapid removal allow for the optimal functioning for each micro plant, as well as of the whole hydropower facility. A solution providing these features represents an advantageous way to modernize micro hydropower plants in conventional construction, enabling the adaptation to current requirements with minimum costs. Meanwhile, the life span of electromechanical components is preserved, as they become unusable should the plant be modernized through integrated alternatives.Configuring a supervisory, control, and data acquisition (SCADA) system for a micro hydropower plant requires an exceedingly complex solution, as many of SCADA features are redundant in this case. Moreover, the implementation cost for such systems, including, perhaps, an IIoT implementation able to solve the communication issues analyzed in  is not jReal-time monitoring of critical controlled plant parameters;Wireless communication for monitored plants;Storage of local value archives for monitored parameters and plant event logs for start-ups, shutdowns, and faults;Performance of basic commands (stopping or starting the micro hydropower plant generator);Provision of feedback when performing computer-launched or plant-generated commands.Therefore, it can be established that a system assuring the basic monitoring and control requirements for a conventional micro hydropower plant must satisfy several conditions:The system presented in this paper provides a modern and versatile solution for remote monitoring and control, assuring wireless communication through GSM support and implementing a message dialogue based on the Message Queuing Telemetry Transport (MQTT) protocol. As a clarification for the readers, this system illustrates a different approach to using common IIoT tools , instead focusing on embedding customized IIoT features to assure stable and performant remote communication. As data transmission is a critical issue in industrial data acquisition systems, although no special complexity of data processing is achieved in this case, IIoT techniques and specific hardware can be included in an industrial data acquisition system architecture. To justify this statement, in the present work, we focus, in particular, on describing a properly implemented hardware structure and ensuring safe communication. The variety of information characterizing a micro hydropower operation mode and the complexity of acquiring and managing its specific parameters suggest the use of a data concentrator that is versatile and reliable enough to allow for both direct data acquisition for a diversity of signal types and communication with other devices from the micro hydropower plant structure. The same architecture must enable commands received from the superior hierarchical level of control to be performed, mainly through digital outputs. The data concentrator, together with the high-level hardware structure and their implemented software application, must correctly perform real-time monitoring and control of the managed structure within the established allowed time limits for the tasks. Equipping the system with hardware to enable the implementation of IIoT communication technologies in a customized application suite can be considered an adequate solution. Compensating the timing limitations by conditioning the data transfer, in addition to providing user feedback while performing commands, would maintain the system stability and its correctness in operation. If such an approach satisfies the performance requirements, no additional advanced solutions or configurations for data processing are needed. Hence, improved function and configuration independence are assured by solely using a data concentrator, a software application for control, and a hardware and software core designed for wireless communication.Unlike an integrated solution, the system can be configured to monitor and control various micro hydropower architectures. The designed application implements a remote monitoring and control core for a micro hydropower plant and can be easily adapted to the particularities of all the plants from a micro hydropower facility, as any plant without an integrated wireless communication infrastructure is eligible for this approach. The hardware design and components of the system are presented in As the main requirements for the designed system have been established, it can be concluded that the hardware and software solution to be implemented must provide means for monitoring the hydrogenerator currents and voltages for the implementation of a basic set of protections. Moreover, the system must provide a means of acquiring the data of interest from other possible specific structures included in the plant, such as temperature or rotational speed sensors. The essential remote-control function must be assured through wireless communication infrastructure involving microsystems providing GSM modems. Several functional units have been established to manage all the necessary hardware architecture. The system can be organized around two sections, i.e., a control section and an executing section located in the two areas corresponding to the situation encountered the field. The first is located at an intermediary command point, and the second is located within the micro hydropower plant architecture.PC-05/104 Process Control [PC-06/104 Process Control industrial system [Regarding the executing component of the system, an efficient infrastructure consisting of industrial devices for data acquisition and control can be configured by using a specialized unit to monito hydrogenerator currents and voltages, in addition to performing complex protection functions. These features can be successfully performed by the  Control  industril system  is adequAs the most versatile and efficient remote communication means is wireless, GSM support is implemented using performant modems suitable for industrial environments. IFB-122 units  are inteThe above-described collection of units and devices established for the implementation of the monitoring and control system under discussion is summarized in The hardware structure was designed based on a practical architecture that already exists in the field. However, it can be used with minimal adaptations to any other conventional micro hydropower plant configuration with similar resources. A diagram of the implemented architecture including the described units is presented in Serial reading commands from the command unit are sent to the modem and transferred through GSM support to the MHA level, where the correspondent modem receives the information and transfers it serially to the data concentrator to further receive the response the concentrator sends back to the command unit. When a command is initiated, the request is sent in the same manner, with data concentrator performing the command by triggering its corresponding digital output.Designing and implementing a hardware infrastructure allowing for remote management of a micro hydropower plant functioning from a command point situated 8–10 km away represents the fundamental feature offered by this system. Apart from a well-structured architecture for acquisition of the necessary data and a compact and easy means of control, an overall effective supervision of plant operation is thus provided. The existence of a robust and efficient communication infrastructure able to manage the various forms of information exchanged between the system nodes is of critical importance for the proper functioning of the implemented structure. An overview of these interactions is presented in As shown in MHC-01.exe) with the role of displaying the centralized acquired information, real-time monitoring of specific element behavior, and assuring their control, which was developed in the Visual C++ environment and runs on Windows operating systems;A high-level software application (mhc-Master.exe and mhc-Slave.exe) developed at the GSM modem level to manage wireless communication implemented using C++ programming language and running on a Linux operating system.Firmware consisting of two complementary applications  running at the command point location features interactive means of displaying and refreshing the real-time monitored signals and events occurring at the micro hydropower plant level. The software provides a collection of schematic diagrams specific to the structure of the monitored plant. A basic set of commands and signalizations is also provided. Moreover, the application features an event log that is updated with each triggered command, in addition to providing essential parameter values that are acquired when the event occurs. Lastly, an extensive archive listing most monitored parameter values is created as MHC-01.exe is operating.The software application  and the timed refresh of the GRAPHICAL UNIT according to the panel selected by the user.As shown in libmosquitto.dev for a Linux operating system), can satisfy the imposed requirements;To implement an IIoT-specific communication protocol; after a thorough analysis for all the possible communication scenarios and the structure of the transferred information, it was concluded that a message queuing telemetry transport (MQTT) protocol, together with its provided library  and at the command point level (command unit), respectively. Their implemented firmware enables dialogue between the PC-06/104 firmware and the MHC-01.exe application. It is imperative for the same firmware to implement the wireless communication characteristics of an IIoT system, namely:PC-06 and the command unit) is extended through the wireless hardware and software infrastructure assured by the command modem and MHA modem.According to this basic scenario, the two complementary applications representing the firmware must be developed and tested in parallel, each dealing with distinct issues of the implemented master/slave dialogue. It can therefore be observed that at the master level (command unit), as the serial command initiator, the publishing of the command message is conditioned by whether serial data have been read or not. Meanwhile, the publishing of the response message from the slave level (PC-06) is conditioned by the of at least one subscription message. Furthermore, the subscription approach differs between master and slave. OnMessage) converts the ASCII message into a binary data buffer. The serial transfer of this buffer is performed in the corresponding main function, which is conditioned by the existence of a valid binary data buffer, thus assuring that the response from the previously published command has been received from the command unit . The specific loop implemented within the master application is shown as a flow chart in The master modem firmware treats the request/response sequence as follows. The subscriber function  modem firmware approaches the request/response sequence differently. The application converts the subscribed message into a binary data packet within the correspondent OnMessage function successively performs a set of actions, including the building of the request packet (TX buffer), reading of the response packet (RX buffer), and saving the RX data within a message buffer.Furthermore, a flow chart illustrating the specific structure of the slave subscriber function is presented in The current trend in IoT application development implies a hardware configuration consisting of a collection of IoT sensor nodes and a managing software for their customization, control, and individual software development support, as presented in . The devFurthermore, performance requirements such as fast command response, timed and fast data refresh, and a stable wireless connection, from both a hardware and software point of view, need to be ensured. At the hardware level, given that at least one of the GSM modems is located at the plant level that is specially adapted to industrial environment systems or devices must be used. IFB-122 modems are designed to operate in extended temperature ranges and ensure resistance to disturbances. Moreover, although the infrastructure is tolerant to medium-quality GSM signals, not requiring intense data traffic, the utilized GSM modems enable the connection of two GSM antennae in case of deterioration of the communication conditions. The modem is disconnected from the broker with which it exchanges messages;The GSM signal is lost (the modem is disconnected from the wireless network);Hazardous events occur, such as stopping the command unit application from the master terminal, or the PC-06 firmware freezes or stops; this case generates a waiting state for both the master and slave , with eventual reconnections due to the lack of activity in the wireless network;A wireless communication environment initiation error occurs in sending messages; in this situation, destroying and recreating the MQTT communication object, along with its reconnection to the broker, represent the most handy and safe method to repair the wireless communication context.From a software point of view, the firmware implemented in the IFB-122 structures must assure, for both master and slave applications, safety reconnecting possibilities in the case of communication errors, such as: mosquitto_loop error) includes several operations: saving the notification error, destroying the MQTT object, resuming the setup process, and preparing the reception buffer to store the serial command. On the contrary, if the loop is successfully refreshed, the program waits for the transmission buffer to be completed, in which case a new command is read and published after the serial transfer of the previous response. In the complementary slave modem application, this type of error is managed in a similar way.A solution to dealing with this kind of error from the software implementation point of view is listed in QOS1 is preferred for the published messages, as it has been proven suitable under the imposed communication conditions. The broker message queue is also ignored, as the subscriber function only processes the currently received message. Adapting the MQTT message communication that is suitable for broadcast to a request/response-based serial communication, which the first must emulate, implies a specific setting configuration and a predefined order for message publishing, with adequate conditioning in the correspondent subscriber function. From the message flow point of view, a one-on-one correspondence between the request message and the response message is mandatory. This is the only way of assuring the expected behavior of the PC-06 unit with respect to the requests sent through the MHC-01 application. In this context, the request messages that did not receive a timely response are set to be ignored, leading to a serial TIMEOUT behavior in the command unit for the sent request. Hence, At the master level, the publishing of each request message is triggered by the reception of the previous response;At the slave level, the publishing of each response message is triggered by a previously received message from the master.Message synchronization is also assured by conditioning the call of the subscriber function upon the appearance of a single published message. In this manner:Regarding communication safety, mainly implying wireless communication, there is a diversity of data security methods that can generally be implemented for IIoT applications. Apart from the usual security approaches implied by the MQTT message transfer protocol, an efficient three-phase authentication protocol for IIoT wireless sensor networks including a PUF chip to ensure the physical security of the devices can be applied for critical data security in IIoT systems, as presented in . With respect to the compact system considered in this work, it can be observed that the transferred data that circulate in the implemented application are binary encrypted according to the implemented data protocol. The significance of the decrypted information is specific to the monitored structure. Thus, the corresponding encryption and decryption is performed offline at the terminal level (command unit for initiative and data concentrator (PC-06) for execution and response, both of which are represented in libmosquitto for the analyzed practical solution, and creating specific algorithms to successfully manage the two-terminal dialogue. In this manner, MQTT involvement in decoding the data remotely transmitted through the Internet is avoided, as well as protocol vulnerabilities. In summary, the discussed levels of encryption, decryption, and decoded information availability are presented in Separating the encryption/decryption process from the wireless data transfer process and using the Linux-compatible firmware suite available on the GSM modems as a software emulator for serial communication provides several advantages. First, the Internet-transferred data have already undergone a sufficiently rigorous encoding process (binary encryption followed by the ASCII conversion requested by the MQTT protocol), the key of which is inaccessible at this level . Moreover, this encoding process allows for supplementary encryption to increase cybersecurity in other situations if necessary. Secondly, the two firmware applications minimally implemented on a Linux operating system concentrate on assuring communication stability, customizing the software instruments provided by This hardware and software organizing strategy has already been tested in several applications implementing bot owner protocol communication and standardized communication.Therefore, it can be concluded that managing the decoding process and information gathering apart from the implemented wireless communication mechanism already assures sufficient data privacy for a set of information specific to the signals of the monitored plant. Furthermore, using different topics for master (/COMMAND) and slave (/DATA), along with the use of an owner broker, provides—in addition to privacy—a better organized message interchange by classifying and ordering their delivery at the broker level. Stricter data control can be further developed easily within the master and slave modem firmware either by implementing a dynamic topic mechanism or by further codifying the sent or received message. Authentication methods and the use of private and public keys are also a means of increasing data security if necessary.Periodic tasks, which are represented by the refresh sequences for various information types provided to the graphical interface and registered in the archive files. A collection of such tasks performs a full refresh of the data gathered by the implemented system. Such updates occur often enough to record all state changes and parameter value modifications but rarely often enough to allow for both the data acquisition and wireless transfer. The testing conditions for the implemented system consider a complete update sequence performed approximately every 20 s and an archive entry registered every 1 min as proper time intervals;Spontaneous tasks, which occur upon user initiative, such as the events generated by the generator start-up/shutdown commands or increasing/decreasing the delivered power. To supervise their execution, confirmation messages are implemented at the graphical interface level. These messages, which warn for a delay of 30 s before the command is performed and the command panel is refreshed on the graphical interface, prevent the user from simultaneously launching commands.According to the establish requirements, it is of critical importance that the designed hardware structure and the corresponding software applications correctly implement a collection of real-time tasks fitting one of the following categories:The task periodicity and command performance duration are tolerant time delays established at the high-level command unit. In this manner, the real-time behavior can be managed by the high-level software application running on a Windows operating system based on the way this aspect is dealt with in a monitoring structure using serial communication. This solution allows for a sufficiently rigorous control, in addition to fitting the time limits set for the implemented system. 1) from the update sequence (S). Whereas the serial transfer time is considered insignificant compared to the wireless data transfer, the moment when T1 is launched is marked by t0, the wireless data transfer  delay is represented by t1C, the terminal execution time for T1 is denoted as t1X, the wireless transfer time of the response for the command unit is marked by t1R, and the remaining time until the next task from sequence S is indicated by t1E. The wireless command transfer time for the next task in sequence S is marked as tnext. The associated diagram is presented in For example, let us consider the periodic task  following tk, both of which are included in S, is programmed to wait until the correspondent tkE expires before being launched.If t2 is launched while sequence S is periodically running, the execution time of T2 depends on the moment from T1 execution when this task is initiated. From the established priority point of view, it is noted that T2 occurs prior to sequence S but not prior to T1; hence, the execution of T2 does not occur until T1 has finished its execution. 2C is the corresponding wireless transfer command to the data concentrator time, t2X is the execution time for T2, t2R is the wireless transfer response to the command unit time, and t2E is the remaining time associated with the command performed at T2. Meanwhile, if spontaneous task T1X′ is the moment at which T2 has been initiated, the T2 execution time (t2) can be calculated as:According to these notations and assuming that t2) stops the data update during its execution and confirmation. However, if the task belonging to the data update has finished its execution before its additional time expires, the command task is executed as soon as it is received;Launching a command :The maximum time required for performing a command occurs when the command request is launched at the beginning of the wireless transfer of the longest periodic refresh task from sequence S, needing the maximum tAs This time interval is taken into consideration when deciding if it is tolerant enough while operating the structure monitored and controlled by the described system.The system was implemented and installed at Zeicani micro hydropower plant, Hidroelectrica, Hațeg, Romania. Micro plant monitoring and control is performed from a command point situated more than 8 km away from the micro hydropower plant. The geographic area around the plant provides a sufficiently stable GSM signal, so the modem placed within the micro hydropower plant is equipped with only one conventional GSM antenna. At the command point level, a system of two GSM antennae is used, as the geographical conditions attenuate the GSM signal strength.MHC-01.exe user application runs at the command point level, providing the following features:Real-time monitoring of the plant functioning parameters;Interactive display of the monitored parameters according to the MHA main diagram and the schematic diagrams of the functioning blocks;Command features such as generator start-up, shutdown, and increasing or decreasing the delivered power, as well as signalizing features for possible occurring faults;Generation of a daily archive storing the values of plant functioning parameters;Generation an event log entry for every start-up, shutdown, or occurring fault.The Windows-compatible MHC-01.exe. The main monitored plant elements  and their defining state and parameters are displayed in the general diagram under generator shutdown conditions . It features a symbolic diagram corresponding to the monitored micro hydropower plant structure, also highlighting the interactions of its main functioning blocks. As pictured in the frame, critical functioning parameter values are displayed at this level . The numerical value display alternates with an interactive display (including information such as oil level (open/closed) and the state of the power network contact (IO)), and significant notifications are also highlighted . A command panel is also featured in this window. The user can initiate generator start-up (START) or shutdown (STOP), increase delivered power (INC.), and decrease delivered power (DEC.). After initiating a command, feedback from the micro hydropower plant level is not sent until the command is executed. The user is notified of the progress of the command performance through the running messages displayed at the bottom of the main frame . After receiving feedback, the interface highlights the performed command. During the functional tests, no command was initiated from the main window, and no MHA fault was been signalized.A secondary panel corresponding to the water-cooling circuit is pictured in A list of monitored temperatures corresponding to the turbine and generator from the main diagram, together with a brief list of generally monitored parameters, can be analyzed in MHC-01.exe starts, data acquisition requests are serially transferred to the GSM modem (master) from the command point. These commands are received by the GSM modem located at the micro hydropower plant (slave) and serially transferred to the PC-06 data concentrator to process the command and serially transfer the response to the slave. The slave further redirects the response to the master, which further serially transfers it to the command unit to refresh the MHC-01 data. Several command and response dialogues between the GSM modems are captured through the remote connection, as shown in When The MHC-01 interface update only occurs after a set of request/response message interchanges assuring that all newly acquired parameter values have been read. When choosing to view a certain panel or a certain parameter table, the values are modified in real time according to the frequency of a new data acquisition. MHC-01.exe also updates the daily archive, a comma-separated value (csv) file available by clicking the “H” button on the main window , as well as for providing remote monitoring and control to micro hydropower plants without integrated wireless communication. The system is compatible with a wide range of micro hydropower plant architectures, providing customization means . The diagrams used for the development of Furthermore, a monitoring software application can be developed to assure the control of several micro hydropower plants in a hydropower facility and, eventually, the control of several facilities in a region. At this level, a web application can be implemented on a server for easier management of several hydropower facilities, with the developed system representing a node in hierarchical hydropower control infrastructure.Although the system and the corresponding implemented software applications are not suitable for situations requiring immediate response to commands or high-frequency data acquisition , this approach finds its utility in monitoring slow processes and initiating commands with permissive execution time.The data concentrator acquires all the information, either directly or from the monitoring devices through serial communication using several protocols, and provides it serially using the MODBUS ASCII standard protocol. Hence, the environmental sensors and transducers do not require integrated wireless communication features. Moreover, data processing is performed offline on a system that does not provide remote monitoring and control features;Because data gathering and processing are performed by PC-06 firmware and the MHC-01 high-level application, few data security measures can be implemented by the wireless communication infrastructure;Additional software resources are minimal, as the modems implement an open-source library-based application on a Linux operating system. Furthermore, no additional software is used to aid in the running of the implemented software suite;From a hardware point of view, the developed system architecture allows for the adaptation to the existing sensor and transducer structure within a micro hydropower plant.The MHC-01 application and system can be considered a low-cost solution due to several important aspects:The presented system can be notably improved by integrating the software infrastructure of the data concentrator in the corresponding modem software application, preserving the strategy of separating the offline coding and decoding of messages from the actual message transfer process. Online access to useful information from the system must remain restricted. Moreover, the developed structure can be installed in various configurations according to the specific situation. For example, if the controlled structure already includes a serial data concentrator, it can be directly connected to the communication modem, with data configuration customized through the software means provided by the MHC-01.exe application. The described architecture was developed starting from the real functioning conditions and configuration of a micro hydropower plant and is currently running at Hidroelectrica, Hațeg, Romania.


Signature verification is the widely used biometric verification method for maintaining individual privacy. It is generally used in legal documents and in financial transactions. A vast range of research has been done so far to tackle different system issues, but there are various hot issues that remain unaddressed. The scale and orientation of the signatures are some issues to address, and the deformation of the signature within the genuine examples is the most critical for the verification system. The extent of this deformation is the basis for verifying a given sample as a genuine or forgery signature, but in the case of only a single signature sample for a class, the intra-class variation is not available for decision-making, making the task difficult. Besides this, most real-world signature verification repositories have only one genuine sample, and the verification system is abiding to verify the query signature with a single target sample. In this work, we utilize a two-phase system requiring only one target signature image to verify a query signature image. It takes care of the target signature's scaling, orientation, and spatial translation in the first phase. It creates a transformed signature image utilizing the affine transformation matrix predicted by a deep neural network. The second phase uses this transformed sample image and verifies the given sample as the target signature with the help of another deep neural network. The GPDS synthetic and MCYT datasets are used for the experimental analysis. The performance analysis of the proposed method is carried out on FAR, FRR, and AER measures. The proposed method obtained leading performance with 3.56 average error rate (AER) on GPDS synthetic, 4.15 AER on CEDAR, and 3.51 AER on MCYT-75 datasets. The biometric system utilizes an individual's physiological or behavioural characteristics for identification, verification, and authentication. The invariable physiological characteristics include DNA, iris, fingerprint, palm, and facial expression , 2, wherBiometric signature systems are involved in two scenarios, namely identification and verification. In the case of signature identification, the task is to retrieve similar signature samples from a signature repository when a signature is provided as a graphical query. In comparison, the signature verification system decides whether the same signer produces a given query signature or not. Thus, the signature verification system is used to classify given handwritten signature samples as genuine or forgeries. The broad categories of forgeries are random, simple, and skilled. This categorization is based on the availability of the user's name and signature to the forger. In the first category, the forger does not have information about both the factors. Due to this reason, the forger presents a signature with a different shape and looks very different in a holistic view. In contrast, the forger knows the user's name in the category of simple forgery. Hence, the forger can produce a much similar signature compared with a genuine signature if a user uses his name or subpart of it as a signature, whereas in the case of skilled forgery, the forger possesses information about the user name and the signature. It helps the forger practice the genuine signature and produces an almost similar signature to the genuine one. Due to this reason, detecting the forged signature in the case of skilled forgery is challenging.Depending on the signature acquisition method, signature verification systems are either online or offline , 7. If tOffline signature verification can follow two different approaches namely writer-dependent and writer-independent . In the In the offline signature verification method, the feature representation is one of the most researched points by the researchers in the past . For feaAn important issue in the training of deep neural networks is the capability of discriminating two visually close signatures, especially in the case of skilled forgery. In the case of skilled forgery, two signatures holistically look similar but only suffer from local deformation, which makes the two signatures dissimilar. It motivates us to devise a novel semi-synthetic approach to add local deformation on the signature for generating the synthetic forged version of the original image. It helps to train the network, which works efficiently to handle the most difficult case of forgery in the case of signature verification.Another fundamental issue is the data-hungry deep learning approaches. The deep learning methods need millions of images to get trained. Ideally, in the case of signature verification, a single genuine image should be present in the repository for verification with query signature image, but in most existing methods, a set of signatures has been taken from the user  to train the deep learning method. However, to get rid of this data need for signature verification, we have mixed the signature data with the handwritten data. We consider the handwritten word as a genuine signature by a writer and the same word by another writer as a forged signature. A generic training has been conducted for the combined signature and word data. It helps to override the need for the vast amount of signature data for the training of the deep learning model for signature verification. Hence, the proposed system is writer-independent, and no separate model has been needed for a particular writer.The rest of the study is organized into five sections. In document analysis research, biometric authentication is referred as the unique identification of a person. This authentication can be categorized based on the behavioural and psychological traits of a person. Another categorization is soft  biometrics and hard  biometrics . Soft biPorwik et al.  used theZouari et al.  proposedDeep convolution neural networks have immensely justified its performance in image classification, natural language processing, and several social media analytics . The touFrom the literature, it has been found that the dynamic signature verification is more efficient than offline signature verification and a widely accepted person's authentication method, but the issues with dynamic signature verification are plenty of samples required to maintain the performance. For mitigating the issues, Daiz et al.  proposedThe overall workflow of the proposed signature verification system is depicted in The basic building block of deep learning frameworks originated from the black-box architecture of deep neural network. A brief idea of the components used for developing the deep neural network model for biometric verification system is mandatory to present in the following subsections.CBk is the kth convolution kernel weights and its bias term, respectively, and is expressing the convolution method.The deep convolutional neural network is multilayered neural network and is recently used in various challenging problems –52. The The operation of convolution is constructed by one or more combination of such kernels. All convolution layers are followed by batch normalization layer and leaky ReLU as activation function in the proposed model.The work , 54 reveThe activation functions in a neural network work as the transfer functions. These layers transform the results of the previous layer to map it with the given ground truth. Two kinds of activation functions are the linear activation function and the nonlinear activation function. In deep neural networks, different nonlinear functions are employed as the activation. These functions are generally introduced to maintain nonlinearity concept in the network. We have adopted various classes of different activation functions as described in the following subsections.(1) Leaky ReLU. It is a linear rectified function, which is in short recall as ReLU. The output of ReLU function is zero for negative input, and otherwise, input remains unchanged . The function corresponding to mathematical representation is given by equation (equation ). In bacequation , and itsequation . The cor(2) Hyperbolic Tangent Activation Function. It is a kind of logistic sigmoid activation function, which has the important interpretation of the biological neurons. The main characteristic of hyperbolic tangent (tanh) function is having higher derivatives vanishing near zero. This is because the hyperbolic tangent function maintains its suitable property to learn the discriminative features from a higher class of varied data samples. The range of the tanh function is in the range of . The tanh function and its derivatives are dispensed in (3) Sigmoid Activation Function. The property of sigmoid activation function yields its normalized score in the range of  at the output scale. The mathematical expression of sigmoid function and its derivatives are explained in the figure below and calculated using equations (quations  and 7),,(3) SigmThe MaxPool layer  is used A preprocessing step is not a vital phase for a convolutional neural network-based system, but it can reduce the total training time and sometimes improve the performance of the system. Besides this, it is also instrumental in representing the input data appropriately for the subsequent phases of the system. In this work, we are incorporating greyscale conversion of colour images and their intensity normalization as prepossessing steps. After converting a colour image into a greyscale image, it is resized such that its smaller side becomes 80 pixels. Besides this, we rotated the images such that the smaller side of the image becomes its height. Finally, its intensities are normalized such that the background pixels on the image became black or near to black, and the foreground pixels (signature pixels) became white or near to white refer to . Here, wTo understand the importance of this phase, let us assume that we have two different signature images of the same signer and try to find out their differences. There are two types of differences between these images: (1) global difference and (2) local difference. The global difference is caused by the shift in the position of signature, size, and shape variance and the orientation of its principal axis, whereas the local difference is caused by the deformation of each pixel in the form of its position displacement and colour intensity changes refer to .In this phase, the proposed system analyzes the global differences by predicting the affine transformation of query signature image with respect to reference signature image. To predict the affine transformation of query image, the proposed system utilizes two trainable neural networks: (1) CNN-1 : convolution neural network and (2) FFNN-1 : feed-forward neural network. The overview of this phase is depicted in ∗64-dimensional vector for each image. These vectors (query image and reference image) are concatenated and passed to the FFNN-1. The FFNN-1 yields different parameters of affine transformation matrix. The architectural and parametric design detail of CNN-1 is given in Here, first of all the query and reference signature image are processed with CNN-1. This network produced 14θrotation ∈ , random shearing with shearing angle θshearing ∈ , and random scale Sx, Sy ∈  for random affine transformation . In this way, we have collected a pair of reference and query image with their corresponding transformation parameters. Utilizing this information, we have trained the affine alignment network.The training of this network section is also a challenging task as we do not have labelled dataset having the affine transformation variation with ground truth. Therefore, we decided to go for a semi-synthetic dataset. Here, we collected signature images from all the datasets under consideration refer to  and handA affine transformation matrix is defined by equation . In our Once the query image and reference image are aligned by transforming the reference image as affine transformation parameter (or transforming the query image as inverse affine transformation), we acquire the local features in both signature images. The local features are acquired by processing these images from the CNN-2. This network is a convolutional neural network, its architecture is depicted in This phase is responsible to handle the local differences in query image and reference image. The feature map (output of a CNN) generated by CNN-2 represents the neighbourhood region of size 44 × 44 pixels of a cell size 4 × 4 pixels. This representation is a 64-dimensional vector for each cell in feature map. Although the affine alignment phase already tackles major alignment issues, the pixel displacement can cause the local misalignment. Therefore, we calculate the Euclidean distance of a cell region in reference image with its 9 corresponding neighbours (3 × 3 window proximity) in the query image. The neighbouring cell in query image having the lowest distance is selected as the match for the corresponding cell in reference image.DMR: distance matching ratio) of number of cells that have lesser matching distance than a predefined threshold (ThMD) with respect to number of cells that have it higher. We can further analyze a signature if it has DMR higher than a predefined threshold (ThDMR). The selection of ThDMR depends upon the extent of extra signature that is allowed. In the proposed work, we have selected it as 4 . If a query signature gets DMR lesser than ThDMR (in our case 4), then we simply discard the query signature. If the query signature passes the ThDMR, then we calculate its similarity score with respect to reference signature.This is the final step in the proposed signature verification system. Here, the matching distance of a cell in reference images is used in making a decision. It is possible that a genuine signature has some portion of signature extra or lesser with respect to reference signature . So, here we need two levels of decision. First, we calculate the ratio  . The datThe results obtained from the proposed work are compared with current state-of-the-art methods on different standard datasets and with different evaluation criteria. We have tested the performance of the system through writer-independent signature verification task considering all reference signatures as a separate entity. We are listing the performance of the proposed system with three evaluation measures such as (1) FRR, (2) FAR, and (3) AER.It stands for false rejection rate, a very important evaluation parameter in the biometric system to measure the likelihood that the biometric-based security system incorrectly rejects the access attempt made by the authentic user of the system. Mathematically (equation ), FRR isFalse acceptance rate or FAR is also a likelihood measure to determine that the biometric system incorrectly accepts the access attempt by the unauthentic user. In terms of mathematical formula, FAR (equation ) of a biThe average error rate or AER is termed as the best threshold value at which the curve of FAR and FRR meets at a point. It generally determines the stability of the system. It is mathematically computed as an average of FRR and FAR as follows:The proposed system has been extensively validated on the three public datasets of signature verification, namely MCYT-75, CEDAR, and GPDS. The proposed method is also compared with other state-of-the-art methods. The evaluation results for the MCYT-75 dataset are summarized in For the CEDAR dataset, the quantitative results, along with the state-of-the-art approaches, are mentioned in The impact of the proposed method for the GPDS synthetic dataset is summarized in 4Generally, signatures are composed of multiple components, and most of them do not provide the necessary information. For example, the date and curved line used below the signature must be ignored since it does not add any information for writer identification. Alternatively, this may help to remove the processing overheads. Interpersonal similarity and high intrapersonal variability are the challenging factors for achieving satisfactory performance to generalize offline signature verification. This may be supposed to extract the most discriminant and stable feature sets from the wide variety of geographical-invariant signers. In this study, we presented a practical verification problem against the forgeries. In the context of feature extraction for writer-independent signature verification, the line-up future directions may be planned to fuse nonhandcrafted features. In the case of adversarial machine learning in the security domain, an interesting future direction can be added to analyze the impact of sharp physical attacks by printing the adversarial noise over the signatures. According to the writer's perspective, another future line can be encouraged to develop a better deep network than the Siamese network and the loss functions to introduce versatile reference signatures. Signature localization is also an important domain that can assist in signature verification in an image.


Agriculture has become an essential field of study and is considered a challenge for many researchers in computer vision specialization. The early detection and classification of plant diseases are crucial for preventing growing diseases and hence yield reduction. Although many state-of-the-artwork proposed various classification techniques for plant diseases, still face many challenges such as noise reduction, extracting the relevant features, and excluding the redundant ones. Recently, deep learning models are noticeable as hot research and are widely used for plant leaf disease classification. Although the achievement with these models is notable, still the need for efficient, fast-trained, and few-parameters models without compromising on performance is inevitable. In this work, two approaches of deep learning have been proposed for Palm leaf disease classification: Residual Network (ResNet) and transfer learning of Inception ResNet. The models make it possible to train up to hundreds of layers and achieve superior performance. Considering the merit of their effective representation ability, the performance of image classification using ResNet has been boosted, such as diseases of plant leaves classification. In both approaches, problems such as variation of luminance and background, different scales of images, and inter-class similarity have been treated. Date Palm dataset having 2631 colored images with varied sizes was used to train and test the models. Using some well-known metrics, the proposed models outperformed many of the recent research in the field in original and augmented datasets and achieved an accuracy of 99.62% and 100% respectively. In the Middle East Area since early times Palms and their fruits have been considered one of the most important crops as well as an essential part of many cultures. One of the important features of palms is that they are evergreen plants as well as their leaves of various ages are present continuously on palm trees throughout the year. So, they are considered hosts of many insects, and they are reliable sources of food. Young and old foliage of palms is preferred for different kinds of insect species. Because the size and the number of fronds in the crown basically stay the same as soon as the crown is fully formed, the amount of food available does not change materially.Among the many varieties of insect species, the red palm weevil (RPW) that can affect coconut palms is considered the most critical pest for palms and was a problem in many countries for a very long time, especially in Gulf region since the 80s. The oil palm yields can be increased by taking care of the health of the palm trees and by early preventing and treating several diseases infections such as fungi, bacteria and, viruses . BecauseRecently, among the many studies in plant disease classification, some have focused on machine learning as a powerful tool. Plant disease classification using machine learning methods mainly consists of three stages: first, remove the background or segment the infected part using preprocessing techniques; second, extract distinguishing features for further classification analysis; finally, supervised or unsupervised algorithms are used to classify the selected features. A convolution net (CNN) is one of the important deep learning algorithms and is the most widely used algorithm for plant leaf disease classification. CNN mainly includes convolutional layers, pooling layers, and fully connected layers. The convolutional layer extracts feature from the local correlation of the information in the image. For the classification task, many CNN-based classification models have been developed in deep learning-related research such as AlexNet, VGGNet, GoogLeNet, ResNet, MobileNet, and EfficientNet. Recently, it was concluded by researchers in deep learning that when the number of deep CNN layers reached a certain depth, it would cause the network to converge more slowly and not improve the classification performance. ResNet network was developed by Microsoft lab in 2015 to solve the problem of gradient elimination or gradient explosion by proposing residual blocks and shortcut connections. ResNet influenced the development direction of deep learning in academic and industry research. The problem of detecting and classifying fruit and vegetable disease using deep learning models by many researchers is reported in the literature. In this section, we will briefly introduce many of the researchers’ contributions related to plant diseases. In .The authors in  proposedFor weed detection in soybean plantations, five deep learning models consists of MobileNetV2, ResNet50, and three proposed models are used by the authors in , and theAlthough the many previous state-of-art studies concerning the use of deep learning models on the detection and classification of plant leaf diseases, still there are gaps to be addressed concerning the use of these models in palm leaf disease detection and classification. In particular, the need for efficient, fast-trained, and few-parameters models without compromising on performance is inevitable. To overcome the above-mentioned problems, three deep learning models are proposed for Palm leaf diseases classification called Residual Network (ResNet) based on , ModifieImplementing a deep learning model by using ResNet for classifying palm leaf diseases.Implementing a modified ResNet Model (MResNet model) by adapting the filter sizes to effectively detect and classify palm leaf diseases.Implementing a transfer learning model by using ResNet (IncResNet model) for classifying palm leaf diseases.Study the effect of different numbers of epochs as a hyperparameter in the training process.Providing comparative analytics of the implemented models with some of the state-of-art models of classifying plant disease.In this research, the work is organized as follows: Section one introduces and summarizes the literature review; Section two presents the methodology used in this research, Section three discusses in detail the results and the comparison of the proposed approach with some of the well-known deep learning models, and finally, Section four gives the conclusion for the proposed study and the suggestion for future research.The proposed palm leaf diseases identification framework is illustrated in In this research, we implement deep neural network models with residual connections to train on the Palm-leaves dataset. Residual connections are considered an effective way in deep neural network architectures to improve gradient flow through the network and ease the training process of it. Simple neural networks that consist of a simple sequence of layers are sufficient for many applications. However, the more complex problems require more complex network architectures that have multiple layers to send inputs to multiple layers and to receive outputs. Some of these types of network architectures are often called directed acyclic graph (DAG) structured-based networks. The residual network is one of a DAG network that has a skip or residual connections between its layers. The residual connections can skip the main network layers for enabling the propagation of parameter gradients more smoothly from the output layer to the earlier layers. This enhances network performance and accuracy while making it possible to train networks more easily. With increasing the depth of the network layers, higher accuracies can be achieved to accomplish difficult tasks such as differentiating between the leaves of Palm Date that contain a very small, infected area of diseases. The three implemented models will be discussed on the following subsections.Data augmentation was frequently used to cover model overfitting problems require a large amount of data for training and hence improving model prediction accuracy. Such model relies on a large amount of data to overcome the problem of overfitting. Due to overfitting, the model is unable to accurately predict cases other than training data. Data augmentation methods can enable machine learning models to be more efficient by creating variations that the model can predict in the real world. In addition, data augmentation was performed using transformation methods to enhance the region of interest (ROI) and to remove any existing noise. The final augmented and improved data are then fed into the fine-tuned implemented models.A ResNet architecture is mainly composed of three types of layers. The first layers are the initial layers, the second are stacks of residual blocks, and the third is the final layers as depicted in The depth of each stack can change from network to network. In our implementation as seen in • A residual network has been created.• The network has been trained.• Classification and prediction on Palm-leaves data have been performed.Using 1x1 convolution odd-size kernel filters in the previous model leads to the features extracted would be fine-grained and local, without any knowledge about the neighboring pixels. In the modified model, we replaced the 1x1 filters with 3x3 convolutional filters in all blocks for different stacks. Moreover, rising the size of 3x3 filters to 5x5 in the blocks will assume large local areas from images to extract many useful features. The architecture of the modified models is displayed in Pretrained networks for image classification have been trained on a huge number of images for classifying images into thousands of different categories. Through the training process, these networks have learned rich features from the training dataset images. The main task of the trained network is to take an image as an input and produce a label for the object in the image. It can compute the probabilities for each object to belong to a specific category.Transfer learning is a common approach used frequently in recent years in deep learning applications . A pre-tThe task of the first convolutional layers of the network is to extract image features for the last classification layers to classify images. More accurately, the last two layers named "Fully Connected Layer" and "Classification Output Layer" in the pre-trained IncResNet network, have the information to classify the objects in images to the predicted labels with the evaluation of the probabilities and the loss values. To re-train a pre-trained network to classify new dataset images, we replace the last two layers with new layers fine-tuned to the new dataset.By replacing the fully connected layer with a new one that matched the number of outputs of our Palm-Leaves classes  the network can learn the new features of these classes. The classification layer of the network classifies the output classes. By replacing the classification layer (without class labels) with a new one, the network can classify the new images into new classes. The network can automatically set the new output classes during the training process. Our network is now ready to be re-trained once more on our set of Palm-Leaves images. Moreover, the weights of earlier layers in the inception network will be frozen by setting the learning rates to zero. During the training process, the inception network does not update the parameters of the layers that have been frozen. This way, not many computations are needed for the gradients of the frozen layers, this may significantly speed up the network training process.The implementation code runs under the Microsoft Windows 10 Home (x64) operating system. The code is written in Matlab 2021b with specific toolboxes. The device used in the implementation is Alienware Aurora R9 desktop equipped with an Octa-core Intel(R) Core (TM) i9-9900 as well as the base frequency of the device is 3.10 GHz. In addition, the device has 32 GB RAM capacity and 1 TB hard disk drive.Palm disease images in this research are used to train and evaluate the proposed deep learning models for the purpose of disease identification and classification from the images. Date Palm data | Kaggle was used for this study. Date Palm data includes three directories: brown spots (470 files), healthy (1203 files), and white scale (958 files). The total images are 2631 colored images with varied sizes.In our experiments, the size of the images is first changed to 192×350×3 for ResNet architectures while for the Inception ResNet architecture, the images are changed to 299×299×3 pixels. The activation function Softmax was chosen in the last layer and loss function was selected as categorical cross entropy. The maximum of epochs was defined in the training of models as 30 epochs. Pre-trained models were used with the same optimization method as used on training of Kaggle dataset. All models use stochastic gradient descent with momentum (SGDM) optimizer. In addition, the learning rate was selected as 0.001 for SGDM algorithm. Validation frequency value for all models was set to 210. During the training, using mini-batch, the weights and gradient can be updated after a subset of the total training set is computed by the models. In this work, mini-batch size was set to 10, which was the maximum value allowed by hardware resources in all models. The seven performance evaluation metrics used for analyzing the models are validation accuracy, training error, validation error, overall precision and recall as well as F1 score. The accuracy metric is defined as:TP and TN are two positive numbers represented the true positive and true negative classifications, respectively, while the positive number T denoted the total number of samples. The precision metric can be defined as:In the above equation, TP and FP represent the true positive and false positive classifications, respectively. The accuracy metrics Recall on and F1Score can be calculated using precision and recall metrics as follows:Where the two positive numbers The training process is accomplished on the dataset with a number of epochs from 5 to 30 and a total number of iterations per epoch is 210 as shown in Since the filter sizes and numbers in each deep learning layer play a necessary role in the accuracy of the network, the proposed MResNet model depends on filters of sizes 3x3 and 5x5. As known, choosing an appropriate filter size mainly affects the feature extraction process and this leads to more validation accuracy with minimal overfitting in the training progress. In this model, an appropriate neighborhood area is considered in the convolution process during the training to overcome the drawbacks of using the small neighborhood area by the first proposed ResNet model. As seen in In our work, the pre-trained IncResNet CNN model  is trainThe comparative analysis of the three implemented models at different epochs is declared in To test the performance evaluation of the three implemented models against some state-of-the-art work, we chose two recent references related to palm leaf disease classification ( and 21]21]). TheThe overall results show that the proposed MResNet is better in classification than the other models in  and 21]21] as weOne of the characteristics of palm disease is that the disease symptoms are usually appear as spotted on the leaves at its nursery stage. So, the main purpose is to develop a system that can detect and separate the infected palm trees earlier to prevent the reduction of palm crops. Deep learning models have become hot models to be used in detecting and classifying plant diseases using images. In this study, two approaches of deep learning have been implemented for Palm leaf disease classification, namely Residual Network (ResNet) and transfer learning of Inception ResNet. The reason to choose the model for palm tree diseases is to take the advantage of ResNet and transfer learning ResNet to train hundreds of layers effectively. Among the implemented deep learning models to classify palm leaf disease, the obtained results show that the proposed MResNet gave higher validation accuracy and reached 100% at different epochs. In addition, the superiority of the MResNet model was proven when compared to some of the recent state-of-the-art deep learning models using some of the well-known metrics. On the other hand, the biggest challenges with using ResNet models for classifying such challenging palm leaves dataset is the model computational density. Because of their heavy computation, ResNets models are mainly run on GPUs. In future studies, the DL model architecture based on one of the appropriate metaheuristic algorithms for the extracting smallest feature subset will decrease the computation cost as well as increase the classification accuracy and can be tested to classify a variety of plant diseases.https://www.kaggle.com/datasets/hadjerhamaidi/date-palm-data.The data that support the findings of this study are openly available in [Date Palm data | Kaggle] at S1 Data(ZIP)Click here for additional data file.


The Pythagorean fuzzy sets conveniently capture unreliable, ambiguous, and uncertain information, especially in problems involving multiple and opposing criteria. Pythagorean fuzzy sets are one of the popular generalizations of the intuitionistic fuzzy sets. They are instrumental in expressing and managing hesitant under uncertain environments, so they have been involved extensively in a diversity of scientific fields. This paper proposes a new Pythagorean entropy for Multi-Criteria Decision-Analysis (MCDA) problems. The entropy measures the fuzziness of two fuzzy sets and has an influential position in fuzzy functions. The more comprehensive the entropy, the more inadequate the ambiguity, so the decision-making established on entropy is beneficial. The COmplex PRoportional ASsessment (COPRAS) method is used to tackle uncertainty issues in MCDA and considers the singularity of one alternative over the rest of them. This can be enforced to maximize and minimize relevant criteria in an assessment where multiple opposing criteria are considered. Using the Pythagorean sets, we represent a decisional problem solution by using the COPRAS approach and the new Entropy measure. Decision-making methods reflect how decisions are completed and how they can be completed better or more successfully. The decision-making process can also be described as evaluating successive decision alternatives and is broadly used in both the social sciences and the more demanding natural sciences and engineering. The fuzzy sets generalizations are involved in the process of decision making by modeling the value of decisional attributes with uncertainty . A very When we have complete and accurate information about each decision attribute and know the crisp values of the decision criteria weights, we deal with decision-making with certainty. On the other hand, when the information is uncertain, the values are unknown or given in some approximation, then we are dealing with decision-making under uncertainty. One approach successfully used to model uncertainty is fuzzy set theory. A fuzzy set is often a functional relationship linking a feature value to a so-called membership function. A domain expert often identifies this function and less often by physical readings. Fuzzy sets as a generalization of classical two-state logic allow better reality modeling, especially in an uncertain environment ,4. FuzzyConsiderable mathematicians put forth exceptional tries to compute the concept of fuzzy sets in various substantial manners. To overcome the confinements of the fuzzy set in managing conflicting statements regarding the enrollment of articles and decision-making, in 1986, Atanassov submitted the intuitionistic fuzzy set . The intAn intuitionistic fuzzy set is a powerful tool for dealing with indeterminate or uncertain information in decision making, mathematical programming tasks, medical diagnosis cases , patternOne way of expressing expert knowledge in MCDA methods is a characteristic objects comparison approach called Characteristic Object METhod (COMET) ,19. HoweThese weights can be assigned arbitrarily by an expert or using a subjective or objective method. In the case of objective weight assignment, the significance of the criteria is examined using a measure such as Entropy or Standard Deviation. In the subjective approach, a domain expert determines the significance of the criteria. The significance of criteria in subjective methods can be expressed by criterion rankings or pairwise criteria comparisons. Subjective weighting methods based on criterion rankings are the Best-Worst Method (BWM) , FUll COAlthough these methods work on crisp values, they cannot be applied to matrices represented using fuzzy logic and extensions. Therefore, new extensions to these methods are proposed to account for uncertain data. Ghorabaee et al. proposed an extension of the SWARA and CRiteria Importance Through Intercriteria Correlation (CRITIC) approach to determine the criterion weights for a matrix represented using fuzzy sets . Lyu et The use of IFS has found wide application in real-life situations due to the excellent modeling properties of human knowledge in decision-making tasks such as public administration, engineering, management science, economics, military, and scientific research.In some real-world problems solved by MCDA methods, it turns out that all the degrees of estimation of the membership and non-membership of the individual alternatives provided by the decision-maker can be determined such that their sum is greater than 1. Such a situation is inappropriate for applying intuitionistic fuzzy sets and makes uncertainty modeling difficult. Therefore, as an extension of intuitionistic fuzzy sets, a Pythagorean fuzzy set (PFS) is presented, which is more flexible in expressing and dealing with uncertainty and imprecision than intuitionistic fuzzy sets in various decision-making procedures.Pythagorean fuzzy sets were initially developed by Atanassov in 1999 using the name “intuitionistic fuzzy sets of the second kind”. Yager presented the first real applications of PFS in decision-making in 2013 . Yang anMCDA provides decision-makers and experts with a wide range of methodologies well suited to the complexity of decision problems. MCDA methods mostly incorporate human participation and judgment. Pythagorean fuzzy sets provide better space for experts to depict their views concerning the vagueness and uncertainty of the considered Multi-Criteria Decision Making (MCDM) issues . Since tPrevious researchers have previously developed multiple MCDA approaches to illustrate the complex choice problems that arise in our daily life. Each choice problem consists of a set of alternatives, criteria, and a vector of weights and types of each criterion (cost or profit). The COPRAS method has been repeatedly applied to uncertainty problems, where uncertainty has been modeled mainly by fuzzy sets. This approach is a suitable and uncomplicated technique to succeed in MCDM problems. The COPRAS approach has been prolonged by countless scholars from the characteristics of composition in the most modern times. This approach estimates the individuality of one alternative over another and is an example of a reasonable equating of alternatives. This approach can maximize and minimize criteria in a study where more than one measure must be evaluated . The COPDue to the vast pool of available tools related to multi-criteria decision analysis, the COPRAS approach has been compared more than once. For example, Özcan and Çelik compared the COPRAS method with the TOPSIS method in a machine selection problem in the food industry in Turkey . PamucarBased on the above review, it can be concluded that the COPRAS method is a promising approach to decision support that has been developed relatively recently. Unfortunately, applications using Pythagorean Fuzzy Sets are pretty limited. Therefore, further work should be conducted towards developing the COPRAS method using entropy measures. The entropy measure in PFS is also an interesting issue, as it is the basis for determining weights in decision matrices in the COPRAS technique. Research towards group decision-making is directed toward aggregating expert knowledge, which is one of the main challenges of group decision-making. Many techniques related to multi-criteria decision analysis provide an answer for a single subjective set of evaluations, so they are extended to the topic of group decision-making. In addition, there is a difficulty associated with incorporating uncertain data into the process of expert knowledge extraction.Some works have omitted research on the sensitivity analysis of the COPRAS method in a PFS environment ;Several papers miss the process of assigning weights in the aggregate preference matrix of Pythagorean Fuzzy Sets decision-makers ;Sensitivity analysis of the proposed entropy methods in Pythagorean Fuzzy Sets is missing;The small number of approaches related to entropy determination in the Pythagorean Fuzzy Sets environment results in a lack of comparisons and accurate statements.Due to the above limitations associated with group decision-making, the motivation of this paper is as follows:This paper focuses on using the Pythagorean Fuzzy COPRAS approach in group decision-making. A new Pythagorean Fuzzy Entropy measure is proposed to determine the attribute weights for the group decision-making problem. The proposed approach is applied to a crop field evaluation problem involving four domain experts. In addition, a sensitivity analysis is performed in this paper to check the accuracy of the proposed approach. The main contribution of our work is applying the new Pythagorean Fuzzy Entropy measure combined with the COPRAS method for crop field evaluation.The rest of the paper is organized as follows. N of nominal elements, K in the crisp set N may be represented as fμ,ϑThe partial derivatives with respect to μ  and ϑ 66 are obtf is increasing with respect to μ when f is decreasing with respect to ϑ when We obtained that, K is less fuzzy than L, i.e., Presently, by using this property of the function, we can conclude that Symmetry: for the property we have  we have ,(7)Ep#AHence, To prove the proposed measure is valid, we have to show that it satisfies the properties as provided in Definition 1.In this section, we use the Pythagorean fuzzy entropy in the COPRAS approach for assessing five agriculture fields Step I: The decision-makers qualitatively expressed the linguistic evaluations for the 11 criteria under consideration rij=1The individual decision matrices received from different decision-makers are then aggregated into one main decision matrix. The resulting aggregated decision matrix is shown in Step IV: In this, we normalize the obtained aggregated pythagrean fuzzy deicion matrix using the given Equation (Equation :(10)rij=The normalized aggregated pythagorean fuzzy decision matrix is presented in Step V: In this step, we will calculate the entropy for the given criteria using the proposed Pythagorean fuzzy entropy, shown in Step VI: Determining the Criteria’s weightConsidering the vector containing the criteria weights has a decisive effect on the ranking order of the alternatives. In the proposed approach, we identify the vector of criteria weights using a newly developed entropy measure.For unknown criteria weights:If the criteria weights are completely unknown, then they are determined using the following Equation :(11)wj=Criteria weights are shown in the After determining the criterion weights and the Pythagorean fuzzy decision matrix, the COPRAS method will evaluate the various alternatives. The flowchart for this method is shown in Step VII: Calculate the weighted decision matrix Step VIII: Calculate the score functionStep IX: Determine the maximizing and minimizing index (B is the set of benefit criteria and ng index  and 14)Step IX: Step X: Determine the relative significance value of each alternative (ernative :(15)Si=gStep XI: Determine the priority order (ty order :(16)Ti=SStep XII: Ranking of the alternatives:The ranking of the alternatives is regulated in declining order based on the values of priority order. The highest final value has the highest rank.By using the In this section, studies on the proposed approach’s sensitivity analysis have been conducted. First, the effect of the alternatives on the values of the obtained weights was investigated. For this purpose, five datasets were created in which one of the possible alternatives The next study related to the sensitivity analysis of the proposed approach was to change the criteria values by a threshold value of Using In this paper, we presented a new Pythagorean fuzzy entropy and its use in group decision-making. It was used to determine the relevance of criteria in an aggregated decision maker preference matrix. It was created because of the benefits of Pythagorean fuzzy sets on better modeling of uncertainty in data. Another aspect addressed in the paper was sensitivity analysis, which confirmed the validity and accuracy of the method used. The results confirmed this approach’s applicability in problems related to crop field evaluation using domain experts’ subjective opinions.In the future, the presented Pythagorean fuzzy sets method can be used in additional applications. For example, the presented strategy can be used in future analyses by applying different fuzzy systems in decision matrices and solving various multi-criteria decision problems with unknown weights. Another research direction could be to use the proposed Pythagorean fuzzy entropy along with other MCDA approaches such as TOPSIS or VIKOR. Additionally, future research would need to address the aspect related to reference models of weights and their reflection by the proposed entropy.