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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.Öğe A Cramer Method for Solving Fully Fuzzy Linear Systems Based on Transmission Average(Payame Noor University (PNU), 2022) Babakordi, Fatemeh; Allahviranloo, TofighSolving fuzzy linear systems has been widely studied during the last decades. However, there are still many challenges to solving fuzzy linear equations, as most of the studies have used the principle of extension, which suffers from shortcomings such as the lack of solution, achieving solutions under very strong conditions, large support of the obtained solutions, inaccurate or even incorrect solutions due to not utilizing all the available information, complicated process and high computational load. These problems motivated us to present a fuzzy Cramer method for solving fuzzy linear equations, which uses arithmetic operations based on the Transmission Average (TA). In this study, fully fuzzy linear systems in the form of à ˜X = ˜B, and dual fuzzy linear systems in the form of à ˜X + ˜B =˜C ˜X + ˜D are solved using the proposed fuzzy Cramer method, and numerical examples are provided to confirm the effectiveness and applicability of the proposed method. © 2022 by the authors.Öğe A fractional multi-wavelet basis in Banach space and solving fractional delay differential equations(Elsevier Ltd, 2024) Savadkoohi, Fateme Rezaei; Rabbani, Mohsen; Allahviranloo, Tofigh; Malkhalifeh, Mohsen RostamyIn this article, we construct a fractional multi-wavelet basis based on Legendre polynomials to solve fractional delay linear and nonlinear differential equations. For this we introduce an orthonormal fractional basis for Banach space L2[0,1] with suitable inner product which make it effective to decrease computational operations and increase accuracy to find approximate solution of the equations. Also, solving fractional problems by orthogonal basis such as Legendre polynomials has a lower accuracy in comparison with fractional basis. Finally, some examples are solved to show the high accuracy of the presented method, and also to compare with some other works. © 2024Öğe A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations(IOP publishing Ltd, 2024) Amoozad, Taher; Abbasbandy, Saeid; Sahihi, Hussein; Allahviranloo, TofighIn this article, a new implementation of the reproducing kernel method is presented for solving systems of fractional-order Volterra integro-differential equations. Unlike previous implementations, this method does not rely on the Gram-Schmidt process. The reproducing kernel method utilizes various components, including space, inner product, bases, and points. Furthermore, the system of fractional-order Volterra integro-differential equations involves Caputo's fractional derivative and Volterra integral. However, when using the reproducing kernel method to solve these systems, challenges such as longer execution time and lower accuracy may arise compared to other methods. The present method has overcome these challenges with features such as easy implementation, high accuracy, and lower execution time.Öğe A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations(Institute of Physics, 2024) Amoozad, Taher; Abbasbandy, Saeid; Sahihi, Hussein; Allahviranloo, TofighIn this article, a new implementation of the reproducing kernel method is presented for solving systems of fractional-order Volterra integro-differential equations. Unlike previous implementations, this method does not rely on the Gram-Schmidt process. The reproducing kernel method utilizes various components, including space, inner product, bases, and points. Furthermore, the system of fractional-order Volterra integro-differential equations involves Caputo’s fractional derivative and Volterra integral. However, when using the reproducing kernel method to solve these systems, challenges such as longer execution time and lower accuracy may arise compared to other methods. The present method has overcome these challenges with features such as easy implementation, high accuracy, and lower execution time. © 2024 IOP Publishing Ltd.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 A precise solution to the shortest path optimization problem in graphs using Z-numbers(American Institute of Mathematical Sciences, 2024) Güner, Nurdoğan; Orhan, Halit; Allahviranloo, Tofigh; Usanmaz, BilalCommunication networks are exposed to internal or external risks that can affect all or part of the system. The most important components that form the infrastructure of these systems are routers, which act as nodes. In the field of graph theory, there are sophisticated techniques that can be used to optimize the path of a packet as it travels through various routers from its origin to its destination. A notable example of such an algorithm is Dijkstra’s algorithm, which is designed to efficiently determine the shortest path. The algorithm works under the assumption that the system operates under ideal conditions. Real-time systems can perform better if risk factors and optimal conditions are taken into account. The relationship between the nodes can be expressed by various metrics such as distance, delay, and bandwidth. The aforementioned metrics facilitate the calculation of the optimal path, with the ultimate objective of achieving low-latency networks characterized by rapid response times. Round-trip time (RTT) can be employed as a metric for measuring enhancements in a range of latency types, including those associated with processing, transmission, queuing, and propagation. The use of Z-numbers was employed in this study to incorporate risk into the optimal path metric. RTT was the preferred metric and reliability was represented by fuzzy linguistic qualifiers. A comparison of several scenarios was shown using a numerical example of a communication network. It is expected that this study will have a significant impact on the evolution from models that consider only ideal conditions to real-time systems that include risks using Z-numbers. © 2024 the Author(s).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 a-Whittaker controllability of ?-Hilfer fractional stochastic evolution equations driven by fractional Brownian motion(Springer Heidelberg, 2023) Ghaemi, Mohammad Bagher; Mottaghi, Fatemeh; Saadati, Reza; Allahviranloo, TofighIn this paper, we study the fractional-order system in the sense of?-Hilfer fractional stochastic evolution equations driven by fractional Brownian motion. Applying the fixed point tech-nique, we prove that there exists a mild solution for the problem and introduce a new type of stability. Finally, we present two examples to demonstrate how the obtained results might be applied.Öğe An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing(Elsevier B.V., 2022) Ghalichi, Shabnam Sadat Seyed; Amirfakhrian, Majid; Allahviranloo, TofighSome efficient radial basis functions (RBFs) have a free parameter called the shape parameter that controls the shape of approximating function. This parameter is mainly selected by trial and error related to the problem. Because of the significant role of this value in the accuracy and stability of the RBF method, we propose an algorithm to choose a good value as a shape parameter. In this work, we focus on the interpolating of scattered data approximation and attempt to find a better value of the shape parameter for RBF interpolation. The proposed algorithm selects a good value for the shape parameter by minimizing a cost function which imitates the error between the radial interpolant and the unknown function f that the data points sampled from the function f. The algorithm can be applied to a multidimensional problem of any dimension and for any radial basis function. Also, many experiments including interpolation of one and two dimensional data sets as well as zooming pictures consider investigating the efficiency of this procedure. Also, we show that this algorithm consistently finds a good value for a shape parameter ?.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 Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator(AMER INST MATHEMATICAL SCIENCES-AIMS, 2022) Akram, Muhammad; Ihsan, Tayyaba; Allahviranloo, Tofigh; Al-Shamiri, Mohammed M. AliThis study presents a new analytical method to extract the fuzzy solution of the fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential equations (FODEs) using the Laplace operator under the strongly generalized Hukuhara differentiability (SGH-differentiability). To this end, firstly the fourth-order derivative of the fuzzy valued function (FVF) according to the type of the SGH-differentiability is introduced, and then the relationships between the fourth-order derivative of the FVF and its Laplace transform are established. Furthermore, considering the types of differentiabilities and switching points, some fundamental theorems related to the Laplace transform of the fourth-order derivative of the FVF are stated and proved in detail and a method to solve FIVP by the fuzzy Laplace transform is presented in detail. An application of our proposed method in Resistance-Inductance circuit (RL circuit) is presented. Finally, FIVP's solution is graphically analyzed to visualize and support theoretical results.Öğe An analytical study of Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy fourier transform under generalized Hukuhara Caputo fractional differentiability(Springernature, 2024) Akram, Muhammad; Yousuf, Muhammad; Allahviranloo, TofighPythagorean fuzzy fractional calculus provides a strong framework for modeling and analyzing complicated systems with uncertainty and indeterminacy. The primary focus of this article is to investigate the analytical solution of the Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy Fourier transform under generalized Hukuhara Caputo fractional differentiability. To this end, we first establish generalized Hukuhara Caputo fractional differentiability in the context of multivariate Pythagorean fuzzy-valued functions and then we present some results of multivariate Pythagorean generalized Hukuhara Caputo fractional differentiability and generalized Hukuhara integrability. We present the concept of multivariate Pythagorean fuzzy Fourier transform and give some results for Pythagorean fuzzy Fourier transforms of second-order generalized Hukuhara partial differentiability. Finally, we provide a practical application of the Pythagorean fuzzy fractional wave equation to visco-elastic materials including polymers and biological tissues. Their graphs are analyzed to visualize and support the theoretical findings.Öğe An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation(Springer, 2024) Ahadi, Azam; Saadati, Reza; Allahviranloo, Tofigh; O'Regan, DonalTo make better decisions on approximation, we may need to increase reliable and useful information on different aspects of approximation. To enhance information about the quality and certainty of approximating the solution of an Apollonius-type quadratic functional equation, we need to measure both the quality and the certainty of the approximation and the maximum errors. To measure the quality of it, we use fuzzy sets, and to achieve its certainty, we use the probability distribution function. To formulate the above problem, we apply the concept of Z-numbers and introduce a special matrix of the form diag(A,B,C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{diag}(A, B, C)$\end{document} (named the generalized Z-number) where A is a fuzzy time-stamped set, B is the probability distribution function, and C is a degree of reliability of A that is described as a value of A*B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A\ast B$\end{document}. Using generalized Z-numbers, we define a novel control function to investigate H-U-R stability to approximate the solution of an Apollonius-type quadratic functional equation with quality and certainty of the approximation.Öğe Application of fuzzy ABC fractional differential equations in infectious diseases(Univ Tabriz, 2024) Babakordi, Fatemeh; Allahviranloo, TofighIn this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can be used for the system of any equations with unknowns.Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.Öğe Application of the reproducing kernel method for solving linear Volterra integral equations with variable coefficients(Iop Publishing Ltd, 2024) Amoozad, Taher; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen RostamyThis article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.Öğe Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems(Springernature, 2024) Rasekhinezhad, Hajar; Abbasbandy, Saeid; Allahviranloo, Tofigh; Baboliand, EsmailThis paper studies the variable fractional functional boundary value problems (VFF-BVPs) by considering Caputo fractional derivative. We use the reproducing kernel method (RKM) without the orthogonalization process as a smart scheme. For this purpose, we construct a reproducing kernel that does not satisfy the boundary condition of VFF-BVP. With this kernel, we can better approximate the solutions for VFF-BVP. Using this method increases the accuracy of the approximate solution so that a significant error analysis can be produced. Finally, two numerical examples are solved to illustrate the efficiency of the present method.Öğe Approximate reasoning(Elsevier, 2024) Pedrycz, Witold; Allahviranloo, TofighThe chapter is focused on the fundamentals of approximate reasoning, their key formal properties, design, and an overall development process. We also show how the mechanisms of approximate reasoning support the construction of rule-based models, which are one of the omnipresent constructs in fuzzy modeling. © 2024 Elsevier Inc. All rights reserved.Öğe Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces(SPRINGER HEIDELBERG, 2022) Eidinejad, Zahra; Saadati, Reza; Allahviranloo, TofighIn this paper, considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural networks with mixed delays (NA-CNN-MD). Our main goal is to investigate the existence of a unique solution for the presented system of NA-CNN-MD in the matrix-valued fuzzy spaces and using the fuzzy measure. After investigating the existence of a unique solution of NA-CNNs-MD which are rho-pseudo almost periodically, we prove the Mittag-Leffler stability and Mittag-Leffler attractiveness for rho-pseudo almost periodic functions. Finally, two examples are given to illustrate the theoretical results.Öğe The best approximation of generalized fuzzy numbers based on scaled metric(HINDAWI LTD, 2022) Allahviranloo, Tofigh; Saneifard, Rasoul; Saneifard, Rahim; Kiani, Farzad; Noeiaghdam, Samad; Govindan, VediyappanThe ongoing study has been vehemently allocated to propound an ameliorated alpha-weighted generalized approximation of an arbitrary fuzzy number. This method sets out to lessen the distance between the original fuzzy set and its approximation. In an effort to elaborate the study, formulas are designed for computing the ameliorated approximation by using a multitude of examples. The numerical samples will be exemplified to illuminate the improvement of the nearest triangular approximation (Abbasbandy et al., Triangular approximation of fuzzy numbers using alpha-weighted valuations, Soft Computing, 2019). A variety of features of the ameliorated approximation are then proved.
