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Öğe Deblurring Medical Images Using a New Grünwald-Letnikov Fractional Mask(IOS Press BV, 2024) Satvati, Mohammad Amin; Lakestani, Mehrdad; Khamnei, Hossein Jabbari; Allahviranloo, TofighIn this paper, we propose a novel image deblurring approach that utilizes a new mask based on the Grünwald-Letnikov fractional derivative. We employ the first five terms of the Grünwald-Letnikov fractional derivative to construct three masks corresponding to the horizontal, vertical, and diagonal directions. Using these matrices, we generate eight additional matrices of size 5 × 5 for eight different orientations: kπ4 , where k = 0, 1, 2, . . ., 7. By combining these eight matrices, we construct a 9 × 9 mask for image deblurring that relates to the order of the fractional derivative. We then categorize images into three distinct regions: smooth areas, textured regions, and edges, utilizing the Wakeby distribution for segmentation. Next, we determine an optimal fractional derivative value tailored to each image category to effectively construct masks for image deblurring. We applied the constructed mask to deblur eight brain images affected by blur. The effectiveness of our approach is demonstrated through evaluations using several metrics, including PSNR, AMBE, and Entropy. By comparing our results to those of other methods, we highlight the efficiency of our technique in image restoration. © 2024 Vilnius University.Öğe Cybersecurity in a Scalable Smart City Framework Using Blockchain and Federated Learning for Internet of Things (IoT)(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Sefati, Seyed Salar; Craciunescu, Razvan; Arasteh, Bahman; Halunga, Simona; Fratu, Octavian; Tal, IrinaHighlights: What are the main findings? Implementation of blockchain enhances the security and scalability of smart city frameworks. Federated Learning enables efficient and privacy-preserving data sharing among IoT devices. What are the implications of the main finding? The proposed framework significantly reduces the risk of data breaches in smart city infrastructures. Improved data privacy and security can foster greater adoption of IoT technologies in urban environments. Smart cities increasingly rely on the Internet of Things (IoT) to enhance infrastructure and public services. However, many existing IoT frameworks face challenges related to security, privacy, scalability, efficiency, and low latency. This paper introduces the Blockchain and Federated Learning for IoT (BFLIoT) framework as a solution to these issues. In the proposed method, the framework first collects real-time data, such as traffic flow and environmental conditions, then normalizes, encrypts, and securely stores it on a blockchain to ensure tamper-proof data management. In the second phase, the Data Authorization Center (DAC) uses advanced cryptographic techniques to manage secure data access and control through key generation. Additionally, edge computing devices process data locally, reducing the load on central servers, while federated learning enables distributed model training, ensuring data privacy. This approach provides a scalable, secure, efficient, and low-latency solution for IoT applications in smart cities. A comprehensive security proof demonstrates BFLIoT’s resilience against advanced cyber threats, while performance simulations validate its effectiveness, showing significant improvements in throughput, reliability, energy efficiency, and reduced delay for smart city applications. © 2024 by the authors.Öğe Effective test-data generation using the modified black widow optimization algorithm(Springer, 2024) Arasteh, Bahman; Ghaffari, Ali; Khadir, Milad; Torkamanian-Afshar, Mahsa; Pirahesh, SajadSoftware testing is one of the software development activities and is used to identify and remove software bugs. Most small-sized projects may be manually tested to find and fix any bugs. In large and real-world software products, manual testing is thought to be a time and money-consuming process. Finding a minimal subset of input data in the shortest amount of time (as test data) to obtain the maximal branch coverage is an NP-complete problem in the field. Different heuristic-based methods have been used to generate test data. In this paper, for addressing and solving the test data generation problem, the black widow optimization algorithm has been used. The branch coverage criterion was used as the fitness function to optimize the generated data. The obtained experimental results on the standard benchmarks show that the proposed method generates more effective test data than the simulated annealing, genetic algorithm, ant colony optimization, particle swarm optimization, and artificial bee colony algorithms. According to the results, with 99.98% average coverage, 99.96% success rate, and 9.36 required iteration, the method was able to outperform the other methods.Öğe Exploring technical efficiency in the European forest sector: A two-stage chance-constrained data envelopment analysis(Elsevier B.V., 2024) Amirteimoori, Alireza; Allahviranloo, Tofigh; Zadmirzaei, MajidThis study analyses the technical efficiency of the forestry sector in Europe which comprises 40 countries. The novelty of this study is the stochasticity of the data and the existence of contextual variables in the two-stage production process of the forest sector. We first developed a two-stage chance-constrained data envelopment analysis model in which the forestry and exploitation stages occur at country-specific levels within the European forest production sector. It was found that the forest management stage is generally more efficient than the exploitation stage and total production at the country-specific level. Contextual variables have a significant impact on efficiency scores, which means that efficiency calculations in the subsequent stage need to be adjusted to take these influences into account. By mitigating these contextual effects, the study improved technical efficiency scores, highlighting top performers like the Russian Federation (DMU31 in North zone), Switzerland (DMU37 in Central-West zone), and Iceland (DMU16 in North zone) with TE scores of 1.0322, 1.0209, and 1.0198 respectively, while also identifying areas for enhancement in countries such as Turkey (DMU38 in South-East zone), Slovakia (DMU33 in Central-East zone), and Romania (DMU30 in Central-East zone) which fall into the lowest three ranks based on their performance with TE scores of 0.5583, 0.5058, and 0.4482 respectively. An important conclusion is that these findings are crucial for policymakers and stakeholders in Europe when developing strategies to improve efficiency and sustainability in the forest sector. © 2024 Elsevier B.V.Öğe Constraint-based heuristic algorithms for software test generation(Elsevier, 2024) Arasteh, Bahman; Aghaei, Babak; Ghanbarzadeh, Reza; Kalan, RezaWhile software testing is essential for enhancing a software system's quality, it can be time-consuming and costly during developing software. Automation of software testing can help solve this problem, streamlining time-consuming testing tasks. However, generating automated test data that maximally covers program branches is a complex optimization problem referred to as NP-complete and should be addressed appropriately. Although a variety of heuristic algorithms have already been suggested to create test suites with the greatest coverage, they have issues such as insufficient branch coverage, low rate of success in generating test data with high coverage, and unstable results. The main objective of the current chapter is to investigate and compare the coverage, success rate (SR), and stability of various heuristic algorithms in software structural test generation. To achieve this, the effectiveness of seven algorithms, genetic algorithm (GA), simulated annealing (SA), ant colony optimizer (ACO), particle swarm optimizer (PSO), artificial bee colony (ABC), shuffle frog leaping algorithm (SFLA), and imperialist competitive algorithm (ICA), are examined in automatically generating test data, and their performance is compared on the basis of various criteria. The experiment results demonstrate the superiority of the SFLA, ABC, and ICA to other examined algorithms. Overall, SFLA outperforms all other algorithms in coverage, SR, and stability. © 2024 Elsevier Inc. All rights reserved.Öğe Cache Aging with Learning (CAL): A Freshness-Based Data Caching Method for Information-Centric Networking on the Internet of Things (IoT)(Multidisciplinary Digital Publishing Institute (MDPI), 2025) Hazrati, Nemat; Pirahesh, Sajjad; Arasteh, Bahman; Sefati, Seyed Salar; Fratu, Octavian; Halunga, SimonaInformation-centric networking (ICN) changes the way data are accessed by focusing on the content rather than the location of devices. In this model, each piece of data has a unique name, making it accessible directly by name. This approach suits the Internet of Things (IoT), where data generation and real-time processing are fundamental. Traditional host-based communication methods are less efficient for the IoT, making ICN a better fit. A key advantage of ICN is in-network caching, which temporarily stores data across various points in the network. This caching improves data access speed, minimizes retrieval time, and reduces overall network traffic by making frequently accessed data readily available. However, IoT systems involve constantly updating data, which requires managing data freshness while also ensuring their validity and processing accuracy. The interactions with cached data, such as updates, validations, and replacements, are crucial in optimizing system performance. This research introduces an ICN-IoT method to manage and process data freshness in ICN for the IoT. It optimizes network traffic by sharing only the most current and valid data, reducing unnecessary transfers. Routers in this model calculate data freshness, assess its validity, and perform cache updates based on these metrics. Simulation results across four models show that this method enhances cache hit ratios, reduces traffic load, and improves retrieval delays, outperforming similar methods. The proposed method uses an artificial neural network to make predictions. These predictions closely match the actual values, with a low error margin of 0.0121. This precision highlights its effectiveness in maintaining data currentness and validity while reducing network overhead. © 2025 by the authors.Öğe Feature-weight and cluster-weight learning in fuzzy c-means method for semi-supervised clustering(Elsevier, 2024) Oskouei, Amin Golzari; Samadi, NeginSemi -supervised clustering aims to guide the clustering by utilizing auxiliary information about the class labels. Among the semi -supervised clustering categories, the constraint -based approach uses the available pairwise constraints in some steps of the clustering procedure, usually by adding new terms to the objective function. Considering this category, Semi -supervised FCM (SSFCM) is a semi -supervised version of the fuzzy c -means algorithm, which takes advantage of fuzzy logic and auxiliary class distribution knowledge. Despite the performance enhancement caused by incorporating this extra knowledge in the clustering process, semi -supervised fuzzy approaches still suffer from some problems. All the data attributes in the feature space are assumed to have equal importance in the cluster formation, while some features may be more informative than others. Thus the feature importance issue is not addressed in the semi -supervised category. This paper proposes a novel SemiSupervised Fuzzy c -means approach, which is designed based on Feature -Weight, and Cluster -Weight learning, named SSFCM-FWCW. Inspired by the SSFCM, a fuzzy objective function is presented, which is composed of (1) a semi -supervised term representing the external class knowledge; (2) a feature weighting; and (3) a cluster weighting. Both feature weights and cluster weights are determined adaptively during the clustering. Considering these two techniques leads to insensitivity to the initial center selection, insensitivity to noise, and consequently helps to form an optimal clustering structure. Experimental comparisons are carried out on several benchmark datasets to evaluate the proposed approach 's performance, and promising results are achieved.Öğe Bipolar fuzzy Fourier transform for bipolar fuzzy solution of the bipolar fuzzy heat equation(University of sistan & baluchestan, 2024) Akram, M.; Bilal, M.; Shahriari, Mohammadreza; Allahviranloo, TofighThis article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology's liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposed methodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics.Öğe Multi-criteria decision making with Hamacher aggregation operators based on multi-polar fuzzy Z-numbers(Elsevier Inc., 2025) Ullah, Inayat; Akram, Muhammad; Allahviranloo, TofighMulti-polar fuzzy sets are crucial for capturing and representing diverse opinions or conflicting criteria in decision-making processes with greater flexibility and precision. While, Z-numbers are important for effectively modeling uncertainty by incorporating both the reliability of information and its degree of fuzziness, enhancing decision-making in uncertain environments. To date, no model in the literature exhibits the properties of multi-polar fuzzy sets and Z-numbers. In this article, we introduce a new concept of multi-polar fuzzy Z-number and Hamacher operations for multi-polar fuzzy Z-numbers. Based on the Hamacher operations, we propose aggregation operators for multi-polar fuzzy Z-numbers, namely, multi-polar fuzzy Z-number Hamacher weighted averaging operator, multi-polar fuzzy Z-number Hamacher ordered weighted averaging operator, multi-polar fuzzy Z-number Hamacher weighted geometric operator and multi-polar fuzzy Z-number Hamacher ordered weighted geometric operator. Additionally, we develop a decision-making model based on the proposed Hamacher aggregation operators. Further, we apply the proposed technique to a couple of case studies to check the validity and authenticity of the proposed methodology. Finally, we compare the outcomes of the study with several existing techniques to assess the accuracy of the proposed model. © 2024 Elsevier Inc.Öğe Optimal nodes localization in wireless sensor networks using nutcracker optimizer algorithms: Istanbul area(IEEE, 2024) Neggaz, Nabil; Seyyedabbasi, Amir; Hussien, Abdelazim G.; Rahim, Mekki; Beşkirli, MehmetNode localization is a non-deterministic polynomial time (NP-hard) problem in Wireless Sensor Networks (WSN). It involves determining the geographical position of each node in the network. For many applications in WSNs, such as environmental monitoring, security monitoring, health monitoring, and agriculture, precise location of nodes is crucial. As a result of this study, we propose a novel and efficient way to solve this problem without any regard to the environment, as well as without predetermined conditions. This proposed method is based on new proposed Nutcracker Optimization Algorithm (NOA). By utilizing this algorithm, it is possible to maximize coverage rates, decrease node numbers, and maintain connectivity. Several algorithms were used in this study, such as Grey Wolf Optimization (GWO), Kepler Optimization Algorithms (KOA), Harris Hawks Optimizer (HHO), Gradient-Based Optimizer (GBO) and Gazelle Optimization Algorithm (GOA). The node localization was first tested in Istanbul, Turkey, where it was determined to be a suitable study area. As a result of the metaheuristic-based approach and distributed architecture, the study is scalable to large-scale networks. Among these metaheuristic algorithms, NOA, KOA, and GWO have achieved significant performance in terms of coverage rates (CR), achieving coverage rates of 96.15%, 87.76%, and 93.49%, respectively. In terms of their ability to solve sensor node localization problems, these algorithms have proven to be effective.Öğe Fuzzy Langevin fractional delay differential equations under granular derivative(Elsevier Inc., 2024) Muhammad, Ghulam; Akram, Muhammad; Hussain, Nawab; Allahviranloo, TofighAnalytical studies of the class of the fuzzy Langevin fractional delay differential equations (FLFDDEs) are frequently complex and challenging. It is necessary to construct an effective technique for the solution of FLFDDEs. This article presents an explicit analytical representation of the solution to the class of FLFDDEs with the general fractional orders under granular differentiability. The closed-form solution to the FLFDDEs is extracted for both the homogeneous and non-homogeneous cases using the Laplace transform technique and presented in terms of the delayed Mittag-Leffler type function with double infinite series. Moreover, the existence and uniqueness of the solutions of the FLFDDEs are investigated using the generalized contraction principle. An illustrative example is provided to support the proposed technique. To add to the originality of the presented work, the FLFDDEs with constant delay are solved by applying vibration theory and visualizing their graphs to support the theoretical results. © 2024 Elsevier Inc.Öğe An outranking method with Dombi aggregation operators based on multi-polar fuzzy Z-numbers for selection of best rehabilitation center(Elsevier B.V., 2025) Ullah, İnayat; Akram, Muhammad; Allahviranloo, TofighUseful decisions are made based on reliable information. The concept of Z-number involves the issue of reliability of information. Multipolar information is particularly important in scenarios involving multiple attributes in a decision making process. There does not exist a study in the literature that conveys multipolar information with reliability. In this research article, the concept of multipolar fuzzy Z-Dombi aggregation operators is first introduced. An outranking method based on the proposed multipolar fuzzy Z-Dombi aggregation operators is then developed. The proposed method is applied to a case study related to the selection of the best rehabilitation centre for the treatment of teenage drug users. The proposed method is compared with four existing techniques in multipolar fuzzy and fuzzy environments to validate the approach. A sensitivity analysis is performed to test the credibility of the study. Further, the Spearman coefficient is calculated for ranking lists obtained by different methods to verify the method's consistency. The study's findings are presented in graphical illustrations for a clear understanding of the results. The method shows validity through consistent comparison with four established techniques. This alignment supports its robustness and relevance in practical applications. Moreover, a positive Spearman correlation coefficient confirms its reliability by aligning rankings with expected outcomes. © 2025 Elsevier Inc.Öğe A Study on Linguistic Z-Graph and Its Application in Social Networks(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Mahapatra, Rupkumar; Samanta, Sovan; Pal, Madhumangal; Allahviranloo, Tofigh; Allahviranloo, TofighThis paper presents a comprehensive study of the linguistic Z-graph, which is a novel framework designed to analyze linguistic structures within social networks. By integrating concepts from graph theory and linguistics, the linguistic Z-graph provides a detailed understanding of language dynamics in online communities. This study highlights the practical applications of linguistic Z-graphs in identifying central nodes within social networks, which are crucial for online businesses in market capture and information dissemination. Traditional methods for identifying central nodes rely on direct connections, but social network connections often exhibit uncertainty. This paper focuses on using fuzzy theory, particularly linguistic Z-graphs, to address this uncertainty, offering more detailed insights compared to fuzzy graphs. Our study introduces a new centrality measure using linguistic Z-graphs, enhancing our understanding of social network structures. © 2024 by the authors.Öğe Effectiveness in fuzzy logic: Applications of fuzzy fractional differential equations(Elsevier, 2024) Allahviranloo, Tofigh; Pedrycz, WitoldIn this chapter, as the effectiveness of fuzzy logic, the fuzzy fractional optimal control problem is studied. For this purpose, the definitions of the fuzzy fractional derivative and the fuzzy optimal control problem are introduced, and the content is completed by some necessary and sufficient conditions for the fuzzy optimal control problem. © 2024 Elsevier Inc. All rights reserved.Öğe Brain magnetic resonance image (MRI) segmentation using multimodal optimization(Springer, 2024) Akan, Taymaz; Oskouei, Amin Golzari; Alp, Sait; Bhuiyan, Mohammad Alfrad NobelOne of the highly focused areas in the medical science community is segmenting tumors from brain magnetic resonance imaging (MRI). The diagnosis of malignant tumors at an early stage is necessary to provide treatment for patients. The patient’s prognosis will improve if it is detected early. Medical experts use a manual method of segmentation when making a diagnosis of brain tumors. This study proposes a new approach to simplify and automate this process. In recent research, multi-level segmentation has been widely used in medical image analysis, and the effectiveness and precision of the segmentation method are directly tied to the number of segments used. However, choosing the appropriate number of segments is often left up to the user and is challenging for many segmentation algorithms. The proposed method is a modified version of the 3D Histogram-based segmentation method, which can automatically determine an appropriate number of segments. The general algorithm contains three main steps: The first step is to use a Gaussian filter to smooth the 3D RGB histogram of an image. This eliminates unreliable and non-dominating histogram peaks that are too close together. Next, a multimodal particle swarm optimization method identifies the histogram’s peaks. In the end, pixels are placed in the cluster that best fits their characteristics based on the non-Euclidean distance. The proposed algorithm has been applied to a Cancer Imaging Archive (TCIA) and brain MRI Images for brain Tumor detection dataset. The results of the proposed method are compared with those of three clustering methods: FCM, FCM_FWCW, and FCM_FW. In the comparative analysis of the three algorithms across various MRI slices. Our algorithm consistently demonstrates superior performance. It achieves the top mean rank in all three metrics, indicating its robustness and effectiveness in clustering. The proposed method is effective in experiments, proving its capacity to find the proper clusters. © The Author(s) 2024.Öğe A software defect prediction method using binary gray wolf optimizer and machine learning algorithms(Pergamon-Elsevier Science, 2024) Wang, Hao; Arasteh, Bahman; Arasteh, Keyvan; Gharehchopogh, Farhad Soleimanian; Rouhi, AlirezaContext: Software defect prediction means finding defect-prone modules before the testing process which will reduce testing cost and time. Machine learning methods can provide valuable models for developers to classify software faulty modules. Problem: The inherent problem of the classification is the large volume of the training dataset's features, which reduces the accuracy and precision of the classification results. The selection of the effective features of the training dataset for classification is an NP-hard problem that can be solved using heuristic algorithms. Method: In this study, a binary version of the Gray Wolf optimizer (bGWO) was developed to select the most effective features of the training dataset. By selecting the most influential features in the classification, the precision and accuracy of the software module classifiers can be increased. Contribution: Developing a binary version of the gray wolf optimization algorithm to optimally select the effective features and creating an effective defect predictor are the main contributions of this study. To evaluate the effectiveness of the proposed method, five real-world and standard datasets have been used for the training and testing stages of the classifier. Results: The results indicate that among the 21 features of the train datasets, the basic complexity, sum of operators and operands, lines of codes, number of lines containing code and comments, and sum of operands have the greatest effect in predicting software defects. In this research, by combining the bGWO method and machine learning algorithms, accuracy, precision, recall, and F1 criteria have been considerably increased.Öğe A new method to solve linear programming problems in the environment of picture fuzzy sets(University of Sistan and Baluchestan, 2022) Akram, Muhammad Saeed; Ullah, Inayat; Allahviranloo, TofighPicture fuzzy set is characterized by neutral membership function along with the membership and non-membership functions, and is, therefore, more general than the intuitionistic fuzzy set which is only characterized by membership and non-membership functions. In this paper, first, we are going to point out a drawback and try to fix it by the existing trapezoidal picture fuzzy number. Furthermore, we define an LR flat picture fuzzy number, which is a generalization of trapezoidal picture fuzzy numbers. We also discuss a linear programming model with LR flat picture fuzzy numbers as parameters and variables and present a method to solve these type of problems using a generalized ranking function. © 2022, University of Sistan and Baluchestan. All rights reserved.Öğe Bipolar fuzzy Fourier transform for bipolar fuzzy solution of the bipolar fuzzy heat equation(University of Sistan and Baluchestan, 2022) Akram, Muhammad Saeed; Bilal, Muhammad Hamza; Shahriari, Mohammadreza; Allahviranloo, TofighThis article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology’s liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposed methodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics. © 2024, University of Sistan and Baluchestan. All rights reserved.Öğe A Comprehensive Survey on Resource Management in 6G Network Based on Internet of Things(Institute of Electrical and Electronics Engineers Inc., 2024) Sefati, Seyed Salar; Haq, Asim Ul; Nidhi; Craciunescu, Razvan; Halunga, Simona; Mihovska, Albena; Fratu, OctavianThe transition to 6th Generation (6G) cellular networks offers significant improvements over 5th Generation (5G), enhancing data transfer, reducing latency, and improving network reliability. Advanced Multiple-Input Multiple-Output (MIMO) technology in 6G boosts network efficiency, particularly benefiting Ultra-Reliable Low-Latency Communications (URLLC). This paper reviews literature on resource management in the Internet of Things (IoT) within the 6G context. We categorize the study into four segments: network-aware resource management, dynamic resource allocation, predictive resource distribution based on traffic and architecture, and energy-centric resource allocation considering IoT device mobility and location. We provide a detailed perspective on current research and highlight future research avenues. Key contributions include a comparative study of IoT resource management techniques, an overview of resource management across LTE, 5G, and 6G networks, insights into applications like Intelligent Transportation Systems (ITS), Industrial IoT (IIoT), and Mobile CrowdSensing (MCS), and an emphasis on upcoming challenges. We emphasize the crucial role of efficient resource management in IoT, particularly in the 6G landscape. © 2013 IEEE.Öğe A bootstrap data envelopment analysis model with stochastic reducible outputs and expandable inputs: an application to power plants(EDP Sciences, 2024) Amirteimoori, Alireza; Allahviranloo, Tofigh; Cezar, AsunurClean production of electricity is not only cost-effective but also effective in reducing pollutants. Toward this end, the use of clean fuels is strongly recommended by environmentalists. Benchmarking techniques, especially data envelopment analysis, are an appropriate tool for measuring the relative efficiency of firms with environmental pollutants. In classic data envelopment analysis models, decision-makers are faced with production processes in which reducible inputs are used to produce expandable outputs. In this contribution, we consider production processes when the input and output data are given in stochastic form and some throughputs are reducible and some others are expandable. A stochastic directional distance function model is proposed to calculate the relative technical efficiency of firms. In order to evaluate firm-specific technical efficiency, we apply bootstrap DEA. We first calculate the technical efficiency scores of firms using the classic DEA model. Then, the double bootstrap DEA model is applied to determine the impact of explanatory variables on firm efficiency. To demonstrate the applicability of the procedure, we present an empirical application wherein we employ power plants. © 2024 The authors. Published by EDP Sciences, ROADEF, SMAI 2024.
