Fuzzy Math
Mohammad javad Agheli; Mohammad Mehdi Zahedi; Marzieh Shamsizadeh
Volume 21, Issue 4 , July and August 2024, Pages 1-21
Abstract
In this article, after the definitions of the reduced hesitant L-fuzzy automaton (RHLFA) and the minimal hesitant L-fuzzy automaton; we convert a hesitant L-fuzzy automaton (HLFA) to an RHLFA by reducing the number of its states such that its language is equal to the original HLFA language. Then, by ...
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In this article, after the definitions of the reduced hesitant L-fuzzy automaton (RHLFA) and the minimal hesitant L-fuzzy automaton; we convert a hesitant L-fuzzy automaton (HLFA) to an RHLFA by reducing the number of its states such that its language is equal to the original HLFA language. Then, by defining an equivalence relation on the monoid X*,we construct an HLFA whose language is equal to the language of the transformed RHLFA, and we show that this HLFA is minimal. In conclusion, we delineate the criteria under which, the number of states in the minimal HLFA is equal to the number of states in the RHLFA
Fuzzy Math
A Hassani Movahed; M Bedrood; Arsham Borumand Saeid
Volume 21, Issue 4 , July and August 2024, Pages 23-34
Abstract
In this paper, we introduce a special types of Z−ideals in MV −algebras and delve into theirproperties. These particular ideals are thoroughly examined within the context of MV −chains,semi-simple MV −algebras and Hyperarchimedean structures. Furthermore, we provide characterizations ...
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In this paper, we introduce a special types of Z−ideals in MV −algebras and delve into theirproperties. These particular ideals are thoroughly examined within the context of MV −chains,semi-simple MV −algebras and Hyperarchimedean structures. Furthermore, we provide characterizations for these ideals, offering equivalent definitions that enhance our understanding of their nature. Our investigation also encompasses the relationships between these special Z−ideals and other types of ideals, such as the minimal prime ideals and the maximal ideals. Overall, this paper aims to provide a comprehensive analysis of special Z−ideals in MV −algebras.
Optimization
Kirti Kirti; Tina Verma; Amit Kumar
Volume 21, Issue 4 , July and August 2024, Pages 35-47
Abstract
Seikh et al. (Iranian Journal of Fuzzy Systems, 18(5) (2021), 155-172) pointed out that there does not exist any approach to solve type-2 fuzzy variable matrix games (matrix games in which each element of the payoff matrix is represented by a type-2 fuzzy variable). To fill this gap, Seikh et al. proposed ...
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Seikh et al. (Iranian Journal of Fuzzy Systems, 18(5) (2021), 155-172) pointed out that there does not exist any approach to solve type-2 fuzzy variable matrix games (matrix games in which each element of the payoff matrix is represented by a type-2 fuzzy variable). To fill this gap, Seikh et al. proposed an approach to solve triangular type-2 fuzzy variable (TT2FV) matrix games (matrix games in which each element of the payoff matrix is represented by a TT2FV). Seikh et al. also solved a real-life TT2FV matrix game (plastic ban problem) to show the applicability of their proposed approach. In future, other researchers may use Seikh et al.’s approach to solve other real-life TT2FV matrix games. However, it is inappropriate to use Seikh et al.’s approach as it may fail to find a correct optimal solution of TT2FV matrix games. To validate this claim, a TT2FV matrix game is solved by Seikh et al.’s approach and it is shown that the obtained optimal solution is not correct. Also, it is pointed out that this inappropriateness occurs as a mathematically incorrect result is considered in Seikh et al.’s approach. Furthermore, Seikh et al.’s approach is modified to resolve its inappropriateness.
Decision Making
Li Shi; Yanlong Yang
Volume 21, Issue 4 , July and August 2024, Pages 49-59
Abstract
This article aims to research the multi-leader-follower games with fuzzy constraint mappings(MLFFGs), in which the feasible strategy mappings of the leaders are fuzzy mappings. By using the Fan-Glicksberg fixed point theorem, an existence theorem of equilibria for the MLFFGs under some conditions is ...
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This article aims to research the multi-leader-follower games with fuzzy constraint mappings(MLFFGs), in which the feasible strategy mappings of the leaders are fuzzy mappings. By using the Fan-Glicksberg fixed point theorem, an existence theorem of equilibria for the MLFFGs under some conditions is obtained. Furthermore, with the assumption of finite rationality, we prove the stable results on the generalized well-posedness, the generalized Tykhonov well-posedness, and the generalized Hadamard well-posedness of fuzzy multi-leader-follower games.
Fuzzy Math
Xiancheng Han; Bin Pang
Volume 21, Issue 4 , July and August 2024, Pages 61-80
Abstract
Considering a complete residuated lattice L as the lattice background, the concept of (preconcave, concave) L-convergence spaces via L-ordered co-Scott closed sets is introduced and its diagonal axioms are proposed. It is shown that concave L-convergence spaces are isomorphic to strong L-concave spaces ...
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Considering a complete residuated lattice L as the lattice background, the concept of (preconcave, concave) L-convergence spaces via L-ordered co-Scott closed sets is introduced and its diagonal axioms are proposed. It is shown that concave L-convergence spaces are isomorphic to strong L-concave spaces in a categorical viewpoint. Also, it is proved that a preconcave L-convergence space satisfies the Kowalsky diagonal axiom if and only if it is concave, and an L-convergence space satisfies the Fischer diagonal axiom if and only if it is concave.
Fuzzy Math
Qiao Lou; Haomin Zhang; Siya Ye
Volume 21, Issue 4 , July and August 2024, Pages 81-100
Abstract
In this paper, our focus is to construct (quasi-)copulas with a given opposite track section. Three different ways for constructing (quasi-)copulas with a given opposite track section are proposed and the best-possible bounds for all those (quasi-)copulas sharing a common opposite track section are also ...
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In this paper, our focus is to construct (quasi-)copulas with a given opposite track section. Three different ways for constructing (quasi-)copulas with a given opposite track section are proposed and the best-possible bounds for all those (quasi-)copulas sharing a common opposite track section are also discussed. Drawing inspiration from the opposite diagonal splicing operation, we propose the curved splicing operation. We obtain that the curved splicing of any two quasi-copulas with a common opposite track section must be a quasi-copula. We also show several sufficient conditionsfor the curved splicing of any two copulas sharing a common opposite track section to be a copula. Furthermore, we discuss the characteristics of a copula constructed by the curved splicing operation. Finally, we construct two novel types of semilinear copulas, and by applying the curved splicing operation we obtain two additional types of semilinear copulas.
Decision Making
Jalal Chachi; Ahmad Kazemifard
Volume 21, Issue 4 , July and August 2024, Pages 101-122
Abstract
Determining weights of criteria is a pivotal challenge that arises in Multi-Attribute Decision Making (MADM) problems. Different methods have been suggested in the literature which can be classified into three main categories: subjective, objective and integrated. Especially when the decision maker does ...
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Determining weights of criteria is a pivotal challenge that arises in Multi-Attribute Decision Making (MADM) problems. Different methods have been suggested in the literature which can be classified into three main categories: subjective, objective and integrated. Especially when the decision maker does not have a specific judgment regarding the weights of the criteria of the decision problem or the number of criteria is large, the methods based on pairwise comparisons are not effective due to the large number of required judgments as well as the natural increase in inconsistency in the judgments. In this paper, we propose an integrated model to determine criteria weights in MADM problems while combining the Ordered Weighted Average (OWA) Yager, entropy, fuzzy/crisp initial decision maker's judgments about the preferences of alternatives, and the information of decision matrix. In this regard, by considering a decision matrix, we formulate the idea as an optimization problem including an extended TOPSIS, L-p metric and $\widetilde{L-p}$ metric, or goal programming model in order to provide an extension of OWA operator and entropy method, simultaneously. Then, we use the proposed method in a real-world dataset to evaluate the priorities of mining opportunities in 17 provinces of Iran (including 235 alternatives by considering 48 criteria). In this regard, a comprehensive list of economic, political, social, strategic and environmental criteria has been used. A full analysis is performed to illustrate the application of the technique that stems from our approach. Finally, we compare the results that we obtain with the results from existing approaches, including Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Simple Additive Weighting (SAW) method and Yager. In this way the accuracy and effectiveness of the presented work is conclusively validated.
Decision Making
Javad Tayyebi; Adrian Deaconu; Elham Hosseinzade; Amir Mohmmad Golmohammadi
Volume 21, Issue 4 , July and August 2024, Pages 123-139
Abstract
The maximum capacity path problem (MCPP) is a classical combinatorial optimizationproblem that seeks to find a path with the maximum capacity in a network. Inthis paper, we consider a fuzzy extension of the MCPP, where the capacities are givenas arbitrary fuzzy numbers. Unlike previous approaches that ...
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The maximum capacity path problem (MCPP) is a classical combinatorial optimizationproblem that seeks to find a path with the maximum capacity in a network. Inthis paper, we consider a fuzzy extension of the MCPP, where the capacities are givenas arbitrary fuzzy numbers. Unlike previous approaches that rely on ranking functionsor specific orderings, we formulate the fuzzy MCPP as a bi-objective path-findingproblem, where one objective is to maximize the nominal capacity and the other is tooptimize the reliability value of the path. We propose an efficient algorithm that canfind a Pareto optimal path for any aggregation function between the two objectives.We also analyze the special case where the network is acyclic and show that the algorithmcan be specialized to run in strongly polynomial time. Furthermore, we presentan application of the fuzzy MCPP to the field of optimal control, where we use a discretizationalgorithm to transform a continuous routing problem into a discrete one andsolve it using the proposed algorithm as a subroutine. To implement this applicationin practice, we run the algorithm on an old real-world project in Iran called Iranrud.Moreover, we report some computational results on grid networks with different sizesthat illustrate the performance of the proposed algorithm.
Computer Science
T. Charan Singh; S. Srithar
Volume 21, Issue 4 , July and August 2024, Pages 141-162
Abstract
Hate speech and hateful language have become more accessible to spread as a result of the increase in social media and digital contacts. Cyberbullying is the term used to describe these kinds of online insults, attacks, and harassment. Regretfully, the prevalence of cyberbullying has increased, with ...
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Hate speech and hateful language have become more accessible to spread as a result of the increase in social media and digital contacts. Cyberbullying is the term used to describe these kinds of online insults, attacks, and harassment. Regretfully, the prevalence of cyberbullying has increased, with those who engage in it hiding behind an illusion of relative online anonymity. Finding such offensive content has become difficult due to the overwhelming amount of user-generated content. Text categorization is a broad field of machine learning. Because deep learning techniques outperform typical machine learning algorithms in various ways, researchers are turning to them to detect cyberbullying. This research proposes a new deep learning (DL)--based technique to overcome the issues of cyberbullying content recognition. To detect and classify the bullying content from pre-processed data using selected essential features, the Deep Kronecker Neural Network (DKNN) technique was employed. Comparing different classification strategies with the proposed approach, the extensive tests conducted on the two datasets demonstrate the significance of this work. We provide a novel technique for cyberbullying detection: the DKNN technique outperforms existing state-of-the-art methods with up to 99.56% accuracy results.
Fuzzy Math
Guojun Wu; Wei Yao
Volume 21, Issue 4 , July and August 2024, Pages 163-177
Abstract
With a complete residuated lattice $L$ as the truth value table, we extend the definition of sobriety of classical convex spaces to the framework of $L$-convex spaces. We provide a specific construction for the sobrification of an $L$-convex space and demonstrate that the full subcategory of sober $L$-convex ...
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With a complete residuated lattice $L$ as the truth value table, we extend the definition of sobriety of classical convex spaces to the framework of $L$-convex spaces. We provide a specific construction for the sobrification of an $L$-convex space and demonstrate that the full subcategory of sober $L$-convex spaces is reflective in the category of $L$-convex spaces with convexity-preserving mappings. Additionally, we introduce the concept of Scott $L$-convex structures on $L$-ordered sets. {\color{blue} As an application of this type of sobriety}, we obtain a characterization for the $L$-join-semilattice completion of an $L$-ordered set: an $L$-ordered set $Q$ is an $L$-join-semilattice completion of an $L$-ordered set $P$ if and only if the Scott $L$-convex space $(Q, \sigma^{\ast}(Q))$ is a sobrification of the Scott $L$-convex space $(P, \sigma^{\ast}(P))$.
Fuzzy Math
Mohammad Mousavi Nasr; Mohammad Sadegh Asgari; Mohsen Ziamanesh
Volume 21, Issue 4 , July and August 2024, Pages 179-195
Abstract
This paper aims to introduce a groundbreaking methodology for deriving analytical solutions to the space-time fractional fuzzy diffusion equation. Our approach uniquely incorporates a Caputo generalized Hukuhara fractional derivative (of order $\beta \in (0,2]$) for the second-order spatial derivative, ...
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This paper aims to introduce a groundbreaking methodology for deriving analytical solutions to the space-time fractional fuzzy diffusion equation. Our approach uniquely incorporates a Caputo generalized Hukuhara fractional derivative (of order $\beta \in (0,2]$) for the second-order spatial derivative, alongside a fuzzy Caputo-Katugampola generalized Hukuhara time-fractional derivative (of order $\alpha \in (0,1)$) for the first-order temporal derivative. The primary objective is to develop explicit and fundamental solutions for both the space-time fractional fuzzy diffusion equation and the time fractional fuzzy diffusion equation, encompassing various forms of fuzzy Caputo-Katugampola generalized Hukuhara time-fractional differentiability. We initiate our study by thoroughly analyzing the fuzzy Fourier and fuzzy $\wp-$Laplace transforms of the equation. To demonstrate the practical utility and effectiveness of our proposed method, we apply it to two specific models: a fuzzy groundwater flow model for computing pressure head, and a fuzzy model for determining the concentration of tumor cells. The results obtained highlight the method's efficiency and precision in addressing the complexities of both the space-time fractional fuzzy diffusion equation and the time fractional fuzzy diffusion equation.
