Article
Computer Science, Theory & Methods
Y. Chalco-Cano, T. M. Costa, H. Roman-Flores, A. Rufian-Lizana
Summary: This article introduces a new characterization of the switching points for generalized Hukuhara differentiability, demonstrating that the set of all switching points is at most countable. Furthermore, new properties in differential calculus are generalized, and new numerical integration methods for interval-valued functions are established based on weaker assumptions than previous results.
FUZZY SETS AND SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
Sunae Pak, Huichol Choe, Kinam Sin, Sunghyok Kwon
Summary: This paper investigates the conditions and solution representation of initial value problems for the fuzzy Bagley-Torvik equation, using the multivariate Mittag-Leffler function. Conditions for solution existence are obtained by converting the fuzzy initial value problem into a cut problem, with examples provided to verify the method's effectiveness. The necessary and sufficient conditions for (1,2)-solutions are also shown in the Appendix.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
Sima Rahimi Chermahini, Mohammad Sadegh Asgari
Summary: This article discusses the solutions of fuzzy wave equations with a focus on the differentiability of solutions, providing examples and examining the efficacy and accuracy of the method.
Article
Multidisciplinary Sciences
Atanaska Tencheva Georgieva, Albena Pavlova
Summary: The study introduces a new double fuzzy transform called the double fuzzy Sawi transform and provides a proof of basic properties of both the single and double fuzzy Sawi transforms. These results are used to obtain the exact solution of a non-homogeneous linear fuzzy telegraph equation with generalized Hukuhara partial differentiability. The validity and superiority of the double fuzzy Sawi transform in solving the fuzzy linear telegraph equation are demonstrated through numerical examples using symmetric triangular fuzzy numbers.
Article
Computer Science, Artificial Intelligence
Manizheh Ghaffari, Tofigh Allahviranloo, Saeid Abbasbandy, Mahdi Azhini
Summary: The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. A new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional wave equation and the fuzzy fractional diffusion equation.
Article
Mathematics
Beatriz Hernandez-Jimenez, Gabriel Ruiz-Garzon, Antonio Beato-Moreno, Rafaela Osuna-Gomez
Summary: This paper addresses the resolution of a fuzzy multiobjective programming problem using level sets optimization, comparing it to other strategies and proposing an algorithm to identify possible Pareto efficient optimal solutions.
Article
Computer Science, Theory & Methods
M. Keshavarz, T. Allahviranloo
Summary: This paper obtains the fuzzy fundamental triangular solution of the fractional diffusion equation under Caputo generalized Hukuhara partial differentiability by using the fuzzy Laplace transform and the fuzzy Fourier transform, and investigates its application in the fuzzy mathematical model of anti-cancer drug release in the tumor.
FUZZY SETS AND SYSTEMS
(2022)
Article
Mathematics, Applied
Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad, Mohammed S. Abdo, Kamal Shah, Thabet Abdeljawad
Summary: This study focuses on analyzing and investigating the conditions for the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation using the Atangana-Baleanu-Caputo fractional derivative methodology. By applying the parametric interval form of the fractional derivative and fixed point theorems, the study examines the existence and uniqueness of solutions and presents numerical examples for validation.
Article
Engineering, Marine
L. Verma, R. Meher, Z. Avazzadeh, O. Nikan
Summary: This paper focuses on developing and analyzing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation (FFKdVE) and confirms the efficacy and effectiveness of the method.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2023)
Article
Multidisciplinary Sciences
Mostafijur Rahaman, Rakibul Haque, Shariful Alam, Sebastian Zupok, Soheil Salahshour, Fariba Azizzadeh, Sankar Prasad Mondal
Summary: This study proposes the type-2 interval context solvability requirements for the initial-valued first differential equation and uses a generalized Hukuhara differentiation approach in analyzing an economic order quantity model in a type-2 interval scenario.
Article
Mathematics, Applied
Saima Rashid, Fahd Jarad, Khadijah M. Abualnaja
Summary: This study focuses on the initial value problem of Hilfer-GPF differential equations in the fuzzy framework, employing the methodology of successive approximation and generalized Lipschitz condition. It investigates FVFIEs with fuzzy initial conditions using generalized fuzzy Hilfer-GPF Hukuhara differentiability, proposing the existence and uniqueness of solutions. The equivalent form of fuzzy FVFIEs is derived to demonstrate convergence, with two examples provided for illustration.
Article
Engineering, Marine
Saima Rashid, Rehana Ashraf, Zakia Hammouch
Summary: This study uses a semi-analytical method called homotopy perturbation transform method (HPTM) to obtain numerical results of nonlinear dispersive and fifth order KdV models in order to investigate the behavior of magneto-acoustic waves in plasma with fuzziness. The method is connected with fuzzy generalized integral transform and HPTM. The study also presents two new results for fuzzy generalized integral transformation involving fuzzy partial gH-derivatives. Illustrative examples are provided to demonstrate the effectiveness and superiority of the proposed method.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2023)
Article
Computer Science, Artificial Intelligence
Khatereh Ebdalifar, Tofigh Allahviranloo, Mohsen Rostamy-Malkhalifeh, Mohammad Hassan Behzadi
Summary: This paper proposes a fuzzy generalized fractional power series method to obtain numerical solutions for a class of fuzzy fractional relaxation problems. The fuzzy generalized fractional power series under different types of the Caputo generalized Hukuhara differentiability are introduced. Some theorems are generalized for the fuzzy generalized fractional power series. The method involves truncating the fuzzy generalized fractional power series of the functions in the relaxation problem and substituting them into the equation. The resulting equation can then be solved, and the unknown fuzzy coefficients can be found. To demonstrate the efficiency of the method, some examples are solved.
Article
Mathematics
Helmut Abels, Felicitas Buerger, Harald Garcke
Summary: This paper studies a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. The properties of solutions are analyzed, focusing on the qualitative evolution of the surface in relation to the mean curvature flow. It is shown that the surface area strictly decreases and an example of a surface that exists for infinite times is given. Mean convexity is conserved while convexity is not. An embedded hypersurface that develops a self-intersection over time is constructed. The interpretation of the equations as a gradient flow is also provided. (c) 2022 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Automation & Control Systems
Bozhang Dong, Tianyang Nie, Zhen Wu
Summary: This work explores a discrete-time mean-field type stochastic optimal control problem and aims to derive the stochastic maximum principle with convex control domains. The L-derivative is utilized to handle the mean-field term, while the adjoint operator technique is employed to overcome the challenges of obtaining adjoint equations and duality relation. The stochastic maximum principle for the discrete-time mean-field type stochastic optimal control problem is successfully established. Additionally, a discrete-time mean-variance portfolio selection problem is solved using a decoupling technique different from the continuous-time case.
Article
Mathematics, Interdisciplinary Applications
N. Shahryari, T. Allahviranloo, S. Abbasbandy
Summary: In this paper, the fuzzy approximate solutions for the fuzzy Hybrid differential equation emphasizing the type of generalized Hukuhara differentiability of the solutions are obtained using the two-dimensional Muntz-Legendre wavelet method. The convergence of the proposed method is established in detail. Numerical results show that the two-dimensional Muntz-Legendre wavelet is very effective and convenient for solving the fuzzy Hybrid differential equation.
NEW MATHEMATICS AND NATURAL COMPUTATION
(2023)
Article
Computer Science, Theory & Methods
Nguyen Thi Kim Son, Hoang Thi Phuong Thao, Tofigh Allahviranloo, Hoang Viet Long
Summary: In this paper, the Caputo fractional LC derivative defined in the linear correlated fuzzy-valued number space RF(A) and its applications in feedback control problem are introduced. The definitions of the Riemann-Liouville-LC integral and the Caputo fractional LC derivative for functions in RF(A) are given, and the properties of the Caputo fractional LC derivative for the sum and difference of two functions are proved. The stability theorems of the equilibrium point in the dynamic systems of space RF(A) are also discussed. Finally, a state feedback control function is built to ensure the asymptotic stability of the equilibrium point in the fractional differential equation system in space RF(A).
FUZZY SETS AND SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Khatereh Ebdalifar, Tofigh Allahviranloo, Mohsen Rostamy-Malkhalifeh, Mohammad Hassan Behzadi
Summary: This paper proposes a fuzzy generalized fractional power series method to obtain numerical solutions for a class of fuzzy fractional relaxation problems. The fuzzy generalized fractional power series under different types of the Caputo generalized Hukuhara differentiability are introduced. Some theorems are generalized for the fuzzy generalized fractional power series. The method involves truncating the fuzzy generalized fractional power series of the functions in the relaxation problem and substituting them into the equation. The resulting equation can then be solved, and the unknown fuzzy coefficients can be found. To demonstrate the efficiency of the method, some examples are solved.
Article
Mathematics, Applied
Mohammad Bagher Ghaemi, Fatemeh Mottaghi, Reza Saadati, Tofigh Allahviranloo
Summary: In this paper, we study a fractional-order system driven by fractional Brownian motion in the sense of?-Hilfer fractional stochastic evolution equations. We use the fixed point technique to prove the existence of a mild solution for the problem and introduce a new type of stability. Finally, we provide two examples to illustrate the application of the obtained results.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Zahra Eidinejad, Reza Saadati, Tofigh Allahviranloo, Chenkuan Li
Summary: The main goal of this article is to investigate the Hyers-Ulam-Rassias stability (HURS) for a type of integral equation called Volterra integral equation with delay (VIE-D). Special functions such as the Wright function (WR), Mittag-Leffler function (ML), Gauss hypergeometric function (GH), H-Fox function (H-F) are considered, and the best control function is selected through numerical calculations to study the stability of the desired equation. The existence of a unique solution and the HURS of the VI-D equation in the matrix-valued fuzzy space (MVFS) with two different intervals are proved using the selected optimal function, i.e., the minimum function. Numerical examples of the obtained results are provided at the end of each section.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
E. Ahmady, T. Allahviranloo, N. Ahmady, S. S. Mansouri
Summary: In this paper, a new solution for hybrid fuzzy differential equations under generalized differentiability is proposed. The method approximates the solution using piece-wise polynomial approximations of degree 3, which may be discontinuous. The existence and uniqueness of the solution, as well as the convergence of the method, are discussed in detail. Several examples are provided to illustrate the approach.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Multidisciplinary Sciences
Bahman Arasteh, Seyed Salar Sefati, Simona Halunga, Octavian Fratu, Tofigh Allahviranloo
Summary: One of the key issues in large distributed systems is timely access to data objects. Replicating data objects across multiple servers is a common method to address this issue. Replica placement, whether static or dynamic, is critical to the effectiveness of distributed systems. This research focuses on reducing data access time, minimizing the number of replicas, and improving the reliability of replica placement algorithms.
Article
Green & Sustainable Science & Technology
Mohammadhanif Dasoomi, Ali Naderan, Tofigh Allahviranloo
Summary: This study examines the determinants of online and offline shopping trip choices in Tehran, Iran, and their implications for urban transportation, the environment, and the economy. A questionnaire survey was conducted to collect data from 1000 active e-commerce users. A deep neural network model was used to predict shopping trip types, achieving the highest accuracy rate of 95.73%. The most important factors affecting shopping trip choices were delivery cost, delivery time, and product price. This study provides valuable insights for transportation planners, e-commerce managers, and policymakers, aiming to promote sustainable development.
Article
Engineering, Multidisciplinary
Muhammad Saqib, Daud Ahmad, Ahmad N. Al-Kenani, Tofigh Allahviranloo
Summary: In this study, novel fourth- and fifth-order iterative schemes for approximating solutions to nonlinear equations in coupled systems using Adomian decomposition methods are proposed. The convergence of the proposed method is examined and numerical examples are provided to demonstrate its effectiveness. Results show that the new schemes are more efficient compared to previous schemes.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Computer Science, Theory & Methods
Muhammad Akram, Ghulam Muhammad, Tofigh Allahviranloo, Witold Pedrycz
Summary: This article introduces the analytical fuzzy solution of the incommensurate non-homogeneous system of fuzzy linear fractional differential equations (INS-FLFDEs) using trivariate Mittag-Leffler functions. The proposed technique reduces uncertainty and complexity of the system. It is validated through applications in electrical networks and mass-spring systems.
FUZZY SETS AND SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Alireza Amirteimoori, Tofigh Allahviranloo, Leila Khoshandam
Summary: This paper introduces a stochastic DEA model based on chance constrained programming to calculate the marginal rates of firms facing data uncertainty. The empirical results from applying the proposed stochastic procedure to sample data on power plants reveal that the results vary at different tolerance levels of chance constraints.
EXPERT SYSTEMS WITH APPLICATIONS
(2024)
Article
Computer Science, Artificial Intelligence
Fazlollah Abbasi, Tofigh Allahviranloo
Summary: This paper presents an extended method of critical path based on fuzzy expert systems for managing schedule uncertainties. The use of generalized quasi-geometric fuzzy numbers to represent activity times, along with a new approach to ranking and measuring the distance of these numbers, is proposed.
GRANULAR COMPUTING
(2023)
Article
Computer Science, Artificial Intelligence
Muhammad Akram, Tayyaba Ihsan, Tofigh Allahviranloo
Summary: This research article discusses the Pythagorean fuzzy fractional differential equations (PFFDE), an important class of modern differential equations. It extends fuzzy fractional differential equations to a Pythagorean fuzzy context and presents a solution procedure for homogeneous and inhomogeneous PFFDEs. The article also explores applications of PFFDE and its graphical representation.
GRANULAR COMPUTING
(2023)
Article
Computer Science, Artificial Intelligence
Nguyen Phuong Dong, Nguyen Thi Kim Son, Tofigh Allahviranloo, Ha Thi Thanh Tam
Summary: This paper investigates a class of fuzzy fractional differential systems with finite-time delay based on the concept of the granular Caputo fractional derivative. The concept of Mittag-Leffler type matrix function generated by a square fuzzy matrix is introduced, and the explicit formula of mild solutions to the problem is constructed through Laplace transform. The existence and uniqueness of fuzzy mild solution of the problem are shown by applying Banach contraction principle. Sufficient conditions are established using Jensen inequality, Holder inequality, and Gronwall inequality to guarantee finite-time stability results of the considered problem, even without Lipschitz property of the function f containing delay term. The theoretical results are illustrated by a numerical example.
GRANULAR COMPUTING
(2023)
Article
Mathematics, Applied
Fatemeh Hasankhani, Behrouz Daneshian, Tofigh Allahviranloo, Farzin Modarres Khiyabani
Summary: In this paper, the concept of the full Z-linear programming problem (FZLP) is introduced and a novel and practical method using the concept of Z-numbers is developed to solve these types of problems. Two illustrative examples are provided to demonstrate the precision and effectiveness of this method.
MATHEMATICAL SCIENCES
(2023)
Article
Computer Science, Theory & Methods
Irina Perfilieva, Shokrollah Ziari, Rahele Nuraei, Thi Minh Tam Pham
Summary: The proposed approach uses the F-transform to construct an operational matrix for solving the Volterra integral equation. The transformed form of the equation reduces to a system of linear equations with a triangular matrix, making the numerical method efficient and low computational. The paper provides proofs of convergence, estimation of computational complexity, and compares the results with other methods using test cases.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Yongliang Yang, Guilong Liu, Qing Li, Choon Ki Ahn
Summary: This paper proposes a novel type of Nussbaum function to handle the feedback control design problem with multiple unknown time-varying control coefficients. By separately compensating the unknown control coefficients and combining with the fixed-time stability theory, the issue of mutual cancellation is resolved and Lyapunov stability analysis becomes feasible. The theoretical discussions and simulation experiments demonstrate the effectiveness of the presented design for continuous-time stochastic nonlinear dynamical systems.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Yingfang Li, Xingxing He, Dan Meng, Keyun Qin
Summary: This paper presents an improved method for estimating the similarity between LR-type fuzzy numbers and compares it with existing methods. The proposed method overcomes the shortcomings of existing methods by considering the shape of LR-type fuzzy numbers.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Tong Kang, Leifan Yan, Long Ye, Jun Li
Summary: This note solves an open problem proposed in the paper Kang et al. (2023) [9] by demonstrating the linearity of set-valued pan-integrals based on a fuzzy measure and the operations pair (+, center dot) through the subadditivity of the fuzzy measure. It also provides an example to show the necessity of the subadditivity condition for the linearity of set-valued pan-integrals. Furthermore, it introduces the pan-integral of set-valued functions based on a fuzzy measure and pan-operations pair (circle plus, circle times).
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Marzieh Shamsizadeh, Mohammad Mehdi Zahedi, Mohamad Javad Agheli Goki
Summary: In this paper, we study a new generalization for the notion of fuzzy automata, called hesitant L-fuzzy automaton (HLFA). The mathematics framework for the theory of HLFA is presented. Moreover, the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA are introduced. Additionally, a minimal complete accessible deterministic hesitant L-fuzzy automaton is presented for recognizing any hesitant L-fuzzy language, and an algorithm is proposed to determine the states of the minimal hesitant L-fuzzy automaton along with its time complexity.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
S. O. Mashchenko
Summary: This paper investigates a fuzzy matrix game with fuzzy sets of player strategies and proposes a method to construct a game value using Zadeh's extension principle and the approach to fuzzy matrix games. It is proved that the fuzzy sets of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set on the real line.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Gustave Bainier, Benoit Marx, Jean-Christophe Ponsart
Summary: The Nonlinear Sector Approach (NLSA) is a method to construct Takagi-Sugeno (T-S) models that precisely represent nonlinear systems with bounded nonlinearities. This paper generalizes the NLSA to polytopic and smooth convex bounding sets, providing new ways to reduce the conservatism of TS representations with interdependent scheduling parameters. Various Linear Matrix Inequalities (LMI) criteria are also provided for stability analysis of these models.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Mi Zhou, Ya-Jing Zhou, Jian-Bo Yang, Jian Wu
Summary: This study proposes a new dissimilarity measure for basic probability assignments (BPAs) in the Dempster-Shafer evidence structure, considering both distance measure and conflict belief. Comparative analysis demonstrates the applicability and validity of the proposed measure, which is further applied to multi-source data fusion and large-scale group decision making.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Nicolas Madrid, Manuel Ojeda-Aciego
Summary: This paper continues the research on the properties of the f-indexes of inclusion and contradiction, and specifically demonstrates the relationship between the two concepts through the reformulated Aristotelian square of opposition.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Hanbiao Yang, Zhongqiang Yang, Taihe Fan, Lin Yang
Summary: This paper discusses the topological structures on fuzzy numbers and their related sets, and investigates the continuity of weighted mean maps with respect to these structures. An application of the results is provided, demonstrating their practical significance.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Narayan Choudhary, S. P. Tiwari, Shailendra Singh
Summary: This paper studies different compositions of (L-fuzzy) automata using category theory and introduces four different categories for the study. It shows that each category has specific properties and advances the existing categories in the field. The monoidal description of these categories enriches the fuzzy automata theory.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Lifeng Li, Qinjun Luo
Summary: In this study, we investigate monotone comparative statics under interval uncertainty. We introduce interval-valued supermodular functions and interval-valued quasisupermodular functions with respect to a partial order relation on intervals. Moreover, we derive some sufficient conditions for monotone comparative statics under interval uncertainty. We also apply these results to analyze the monotone comparative statics of interval games with strategic complements.
FUZZY SETS AND SYSTEMS
(2024)
