Fuzzy Math
LeSheng Jin; Ronald R. Yager; Chao Ma; Reza Langari; Chiranjibe Jana; Radko Mesiar; Humberto Bustince
Volume 21, Issue 5 , September and October 2024, Pages 1-9
Abstract
The concepts of cognitive interval information and cognitive uncertain information, which are two recently proposed types of uncertain information, have been extended in this work to the typical hesitant fuzzy environment. We introduce the notions of typical hesitant monopolar cognitive interval information ...
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The concepts of cognitive interval information and cognitive uncertain information, which are two recently proposed types of uncertain information, have been extended in this work to the typical hesitant fuzzy environment. We introduce the notions of typical hesitant monopolar cognitive interval information and typical hesitant cognitive uncertain information. To facilitate their analysis, we define uncertainty degree functions and score functions for these concepts using extended aggregation operators. Furthermore, we reanalyze some decision models discussed in earlier literature using these newly proposed concepts to demonstrate their advantages and potential applications.
Engineering
Zi-hong Huang; Yong Liu; Chang-cheng Ji
Volume 21, Issue 5 , September and October 2024, Pages 11-30
Abstract
Unmanned aerial vehicle (UAV) safety inspection is a developing technology that offers the benefits of high efficiency, low cost, and freedom from dangerous areas and unique situations. An urgent fundamental issue in the deployment of UAV in factories is how to successfully strike a balance between the ...
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Unmanned aerial vehicle (UAV) safety inspection is a developing technology that offers the benefits of high efficiency, low cost, and freedom from dangerous areas and unique situations. An urgent fundamental issue in the deployment of UAV in factories is how to successfully strike a balance between the effectiveness and cost of UAV safety inspection. In view of this, we build a route planning model for UAV inspection. And then, by using the path planning of UAV safety inspection as the research object, based on the two important evaluation indicators of cost and efficiency, we exploit fuzzy time window and adaptive genetic algorithms to design the solution algorithm. Finally, a case verifies the applicability and logic of the proposed model. The results show that the proposed path optimization model with fuzzy time window can reasonably pass all inspection points under balanced conditions, and the hybrid genetic algorithm has good optimization ability.
Fuzzy Math
X.Y. Wu; Yi-Wei Huang
Volume 21, Issue 5 , September and October 2024, Pages 31-49
Abstract
In the framework of L-convex spaces, this paper is aim to study fuzzy convergence structuresof L-convex space in a viewpoint of fuzzy relations. For this purpose, L-directed relation is introducedand some of its examples are proposed. Based on this, notions of L-convergence relation and L-convex convergence ...
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In the framework of L-convex spaces, this paper is aim to study fuzzy convergence structuresof L-convex space in a viewpoint of fuzzy relations. For this purpose, L-directed relation is introducedand some of its examples are proposed. Based on this, notions of L-convergence relation and L-convex convergence relation are introduced. It is proved that there is a Galois's connection between the category of L-convergence relation spaces and the category of L-convex enclosed relation spaces. In particular, L-convex convergence relation spaces and L-convex enclosed relation spaces are categorically isomorphic. Also, notions of L-ideal-convergence structure and L-convex ideal-convergence structure are introduced. It is proved that L-convergence relation spaces and L-ideal-convergence spaces are categorically isomorphic. In particular, L-convex convergence relation spaces and L-convex ideal-convergence spaces are categorically isomorphic.
Fuzzy Math
Amin Ghodousian; Sara Zal
Volume 21, Issue 5 , September and October 2024, Pages 51-69
Abstract
This paper presents some novel theoretical results as well as practical algorithms and computational procedures on continuous fuzzy relational equations programming problems. The fuzzy relational programming problem is a minimization (maximization) problem with a linear objective function subject to ...
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This paper presents some novel theoretical results as well as practical algorithms and computational procedures on continuous fuzzy relational equations programming problems. The fuzzy relational programming problem is a minimization (maximization) problem with a linear objective function subject to fuzzy relational equalities or inequalities defined with certain algebraic operations. In the literature, the commonly seen frameworks for such optimization models are to assume that the operation takes minimum t-norm, strict continuous t-norms (e.g., product t-norm), nilpotent continuous t-norms (e.g., Lukasiewicz t-norm) or Archimedean continuous t-norms. Based on new concepts called partial solution sets, the current paper considers this problem\textbf{ }in the most general case where the fuzzy relational equality constraints are defined by an arbitrary continuous t-norm and capture some special characteristics of its feasible domain and the optimal solutions. It is shown that the current generalized results are automatically reduced to (apparently) different ones that hold for special operators when continuous t-norm is replaced by strict, nilpotent or Archimedean continuous t-norm. Also, the relationship between the results derived here and those of previous publications regarding this subject is also discussed. Finally, the proposed algorithm is outlined and illustrated by a numerical example where the continuous fuzzy relational equations is defined by Mayor-Torrens operator that is not an Archimedean t-norm (and then, neither strict nor nilpotent).
Fuzzy Math
Kar Samarjit; Bikash Koli Roy; Manas Kumar Mohanty
Volume 21, Issue 5 , September and October 2024, Pages 71-88
Abstract
In this paper, we introduce a new concept of fuzzy extropy measure, which can help to measure any system's uncertainty or fuzziness in parallel to fuzzy entropy. Fuzzy extropy can be considered as a dual concept of fuzzy entropy. Additionally, we provide ideas for higher-order fuzzy extropy and hybrid ...
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In this paper, we introduce a new concept of fuzzy extropy measure, which can help to measure any system's uncertainty or fuzziness in parallel to fuzzy entropy. Fuzzy extropy can be considered as a dual concept of fuzzy entropy. Additionally, we provide ideas for higher-order fuzzy extropy and hybrid fuzzy extropy. Then, we introduce concepts of credibilistic extropy for both discrete and continuous fuzzy variables. Furthermore, we have provided examples of these concepts and compared the extropy results with existing fuzzy entropy results. Finally, the validation through simulation studies offers a visual representation of extropy parameters and density distributions, providing empirical insights into the proposed measures' behavior and enhancing their credibility and understanding.
Optimization
Ali Abbasi Molai
Volume 21, Issue 5 , September and October 2024, Pages 89-104
Abstract
This paper introduces a system of Fuzzy Relation Inequalities (FRIs) with the max-min-product composition operator. To determine the structure of solution set of the system, we firstly focus on a single inequality and study its solution set and properties. Then, the structure of solution set of the system ...
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This paper introduces a system of Fuzzy Relation Inequalities (FRIs) with the max-min-product composition operator. To determine the structure of solution set of the system, we firstly focus on a single inequality and study its solution set and properties. Then, the structure of solution set of the system is determined by the points. The necessary and sufficient conditions are proposed for its consistency. Some useful properties of the system of the max-min-product FRIs are presented to determine the structure of its minimal solutions. A latticized linear programming problem is proposed with constraints as FRIs using the max-min-product composition. It is shown that one of its optimal solutions can be given in terms of a closed form. Based on the closed form, a matrix-based-algorithm with a polynomial computational complexity is designed to find one of its optimal solutions. A practical example is presented to illustrate the system and the optimization problem in the area of data transmission mechanism.
Fuzzy Math
H Hashemi; Reza 09123618518 Ezzati; nasser mikaeilvand mikaeilvand; M Nazari; Reza Ezzati
Volume 21, Issue 5 , September and October 2024, Pages 105-119
Abstract
This paper presents a novel approach for modeling and analyzing complex systems withuncertain data by using fuzzy calculus and time-fractional di erential equations. Speci cally,we propose the use of the fuzzy Atangana-Baleanu time-fractional derivative with non-singularkernels for fuzzy functions as ...
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This paper presents a novel approach for modeling and analyzing complex systems withuncertain data by using fuzzy calculus and time-fractional di erential equations. Speci cally,we propose the use of the fuzzy Atangana-Baleanu time-fractional derivative with non-singularkernels for fuzzy functions as a suitable fractional derivative type for the qualitative analysis offractional di erential equations in fuzzy space. Additionally, we provide a method for numer-ically solving fuzzy linear time-fractional equations in uid dynamics using the fuzzy Laplacetransform iterative method. The e ectiveness and practical relevance of our proposed methodare demonstrated through concrete examples, including the fuzzy time-fractional Advection-Dispersion equation, the fuzzy time-fractional Navier-Stokes equation, and Couette ow .These examples showcase the potential of our method to address real-world problems in uiddynamics and provide a clear illustration of the solution steps involved. Our ndings high-light the importance of considering fuzzy calculus and time-fractional di erential equations inmodeling and analyzing complex systems with uncertain data.
Industrial Engineering
salim ziani; Tarek Ahmed_ali; Tennache Nadji; Abdennour Benlahreche
Volume 21, Issue 5 , September and October 2024, Pages 121-132
Abstract
Security and con dentiality of our information such as access codes bank or postal accounts are becoming more and more important to protect against espionage by foreigners. There are several researches to improve the security of the user's personal information when entering the password, or saving, ... ...
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Security and con dentiality of our information such as access codes bank or postal accounts are becoming more and more important to protect against espionage by foreigners. There are several researches to improve the security of the user's personal information when entering the password, or saving, ... etc. The objective of this paper is to create a novel virtual keyboard display system based on a random display algorithm, in order to have a keyboard with random combinationsof the virtual display matrix. This work focuses on the introduction of fuzzy systems mixed with the random number generation. Fuzzy systems use the values of the pressure forces exerted by the user or the operator on the virtual keyboard touchscreen as inputs to the fuzzy systems. The fuzzy system is designed by using the time-varying fuzzy sets. We use the "modulo operator" algorithm to generate a random integer. For the realization, we use a microcontroller (ESP8266 node MCU.V3 microcontroller) and the touchscreen (ili9341) to display a 4X4 numeric matrix to enter a standard four-digit code.
Fuzzy Math
Srilekha R; Parthiban V; Dhanasekar sundaram
Volume 21, Issue 5 , September and October 2024, Pages 133-150
Abstract
This study is concerned with finding the controllability of granular type-2fuzzy fractional-order dynamical control systems (GrT2FuFDCS) usingMittag-Leffler matrix function. Some new concepts concerning to granularinterval valued type-2 fuzzy fractional derivative is introduced inthis paper. To arrive ...
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This study is concerned with finding the controllability of granular type-2fuzzy fractional-order dynamical control systems (GrT2FuFDCS) usingMittag-Leffler matrix function. Some new concepts concerning to granularinterval valued type-2 fuzzy fractional derivative is introduced inthis paper. To arrive at finding the controllability of the type-2 fuzzydynamical system, type-2 triangular fuzzy function and type-2 triangularfuzzy numbers are used to model fractional dynamical controlsystem. Besides, the controllability Grammian matrix is defined basedon Mittag-Leffler matrix function. Granular fuzzy Laplace transform andinverse Laplace transform are utilized to derive the solution of the type-2 triangular fuzzy fractional-order control systems. The derived resultsensure that the controllability of the proposed GrT2FuFDCS for bothlinear and non-linear case exists. Finally, numerical examples and theirsimulation results are given to illustrate the merit of the obtained results.
Optimization
Amin Ghodousian; Sara Zal
Volume 21, Issue 5 , September and October 2024, Pages 151-174
Abstract
In this paper, we investigate nonlinear optimization problems whose constraints are defined as fuzzy relational equations (FRE) with max-min composition. Since the feasible solution set of the FRE is often a non-convex set and the resolution of the FREs is an NP-hard problem, conventional nonlinear approaches ...
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In this paper, we investigate nonlinear optimization problems whose constraints are defined as fuzzy relational equations (FRE) with max-min composition. Since the feasible solution set of the FRE is often a non-convex set and the resolution of the FREs is an NP-hard problem, conventional nonlinear approaches may involve high computational complexity. Based on the theoretical aspects of the problem, an algorithm (called FRE-ACO algorithm) is presented which benefits from the structural properties of the FREs, the ability of discrete ant colony optimization algorithm (denoted by ACO) to tackle combinatorial problems, and that of continuous ant colony optimization algorithm (denoted by ACOR) to solve continuous optimization problems. In the current method, the fundamental ideas underlying ACO and ACOR are combined and form an efficient approach to solve the nonlinear optimization problems constrained with such non-convex regions. Moreover, FRE-ACO algorithm preserves the feasibility of new generated solutions without having to initially find the minimal solutions of the feasible region or check the feasibility after generating the new solutions. The FRE-ACO algorithm has been compared with some related works proposed for solving nonlinearoptimization problems with respect to max-min FREs. The obtained results demonstrate that the proposed algorithm has a higher convergence rate and requires a less number of function evaluations compared to other considered algorithms.
