Fuzzy Math
Jean De La Croix SAMA; Kounhinir SOME
Volume 21, Issue 2 , March and April 2024, Pages 1-18
Abstract
In this work, we present a novel approach for resolving a fuzzy single-objective function with fuzzy constraints. The algorithm of the method is based on the null set concept and is focused on minimizing cases. With the null set concept, two partial subtraction orders for fuzzy numbers have been defined, ...
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In this work, we present a novel approach for resolving a fuzzy single-objective function with fuzzy constraints. The algorithm of the method is based on the null set concept and is focused on minimizing cases. With the null set concept, two partial subtraction orders for fuzzy numbers have been defined, namely simple subtraction and the Hukuhara difference. That allows us to define, respectively, optimal solutions and H-optimal solutions. First, the initial optimization problem is transformed into a deterministic, nonlinear, bi-objective optimization problem. Then, Karush Kuhn Tucker's (KKT) optimality conditions are applied to find deterministic optimal solutions. Finally, a few fuzzy algebraic operations are employed to transform deterministic optimal solutions into fuzzy optimal solutions for the initial solutions. In order to demonstrate the effectiveness of the approach, we have dealt with eleven test problems from the literature. Our method has been compared to those of other methods, and our method is at least the best in each instance.
Fuzzy approximation
Reza Ezzati; Samaneh Zabihi
Volume 21, Issue 2 , March and April 2024, Pages 19-34
Abstract
This paper introduces a novel approach to obtaining analytical solutions forfuzzy fractional differential equations in the context of weighted Caputo-type generalizedHukuhara derivatives. The paper proposes the use of non-singular kernels to improve theaccuracy of fractional calculus in fuzzy space and ...
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This paper introduces a novel approach to obtaining analytical solutions forfuzzy fractional differential equations in the context of weighted Caputo-type generalizedHukuhara derivatives. The paper proposes the use of non-singular kernels to improve theaccuracy of fractional calculus in fuzzy space and establishes the uniqueness of solutions forfuzzy fractional differential equations. The paper also introduces the concept of fuzzy Laplacetransforms to facilitate the solution of these equations. Practical examples, such as the fuzzyfractional Newton’s law of heating and cooling, are provided to demonstrate the effectivenessof the proposed method. Overall, this paper contributes to the development of practical solutionsfor real-world problems in fuzzy space and enhances the accuracy of fractional calculusin this context.
Decision Making
Ljubica Mudric-Staniskovski; Ljubica Djurovic; Nenad Stojanovic
Volume 21, Issue 2 , March and April 2024, Pages 35-49
Abstract
In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the $\lambda$-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. ...
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In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the $\lambda$-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems.
Decision Making
Derya Bakbak; Vakkas Ulucay; S. A. Edalatpanah
Volume 21, Issue 2 , March and April 2024, Pages 51-65
Abstract
The present study aims to described the concept of trapezoidal fuzzy multi number aggregation operators and also provide its application in architecture. Our main focus is on the trapezoidal fuzzymulti number weighted arithmetic average (TFMNWAA) operator, the trapezoidal fuzzy multi numberweighted geometric ...
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The present study aims to described the concept of trapezoidal fuzzy multi number aggregation operators and also provide its application in architecture. Our main focus is on the trapezoidal fuzzymulti number weighted arithmetic average (TFMNWAA) operator, the trapezoidal fuzzy multi numberweighted geometric average (TFMNWGA) operator and trapezoidal fuzzy multi-number hybrid aggregation (TFMNHA) operator along with their developable properties. Then the notion of the score function of ranking the trapezoidal fuzzy multi numbers is defined. We apply the TFMNHA operator to multi criteria decision making trapezoidal fuzzy multi number. Finally, a comparative analysis is presented with a numerical example is provided to show its applicability and usefulness.
Optimization
Marzieh Mortezaee; Mehdi Ghovatmand; Alireza Nazemi
Volume 21, Issue 2 , March and April 2024, Pages 67-85
Abstract
In this paper, a new approach based on fuzzy systems is used for solving variable-order fractional delay differentialalgebraic equations. The fractional derivatives are considered in the Atangana-Baleanu sense that is a new derivativewith the non-singular and non-local kernel. By relying on the ability ...
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In this paper, a new approach based on fuzzy systems is used for solving variable-order fractional delay differentialalgebraic equations. The fractional derivatives are considered in the Atangana-Baleanu sense that is a new derivativewith the non-singular and non-local kernel. By relying on the ability of fuzzy systems in function approximation,the fuzzy solutions of variables are substituted in variable-order fractional delay differential algebraic equations. Theobtained algebraic equations system is then transformed into an error function minimization problem. A learningalgorithm is used to achieve the adjustable parameters of fuzzy solutions. It is shown that the variable-order fractionaldelay optimal control problems can be reformulated as variable-order fractional delay differential algebraic equationsand solved by the proposed method. The efficiency and accuracy of the presented approach are assessed through someillustrative examples of the variable-order fractional delay differential algebraic equations
Computer Science
Huiru Cheng
Volume 21, Issue 2 , March and April 2024, Pages 87-104
Abstract
A new similarity/distance measure based on the centre of nine-point circle of the isosceles triangular fuzzy numbers is recommend in this paper. Extend the similarity/distance measure based on centroid, orthocenter, circumcenter, incenter and nine-point circle center of the isosceles triangles. It is ...
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A new similarity/distance measure based on the centre of nine-point circle of the isosceles triangular fuzzy numbers is recommend in this paper. Extend the similarity/distance measure based on centroid, orthocenter, circumcenter, incenter and nine-point circle center of the isosceles triangles. It is proved that this general similarity/distance measure conforms to the properties of distance. Subsequently, some examples are presented to justify the superiority and validity of the proposed similarity/distance measure between IFSs based on the center of nine-point circle, which demonstrate that this measure overcomes the disadvantage of the existing similarity measures. The application of the proposed similarity measure to deal with pattern recognition problems is described, and the results are correlated with those reported in some prevailing studies. In addition, a clustering technique to classify objects based on the proposed similarity measure is discussed. Through a detailed comparative analysis of some existing measures, it is concluded that some of the existing measures fail to discriminate the results obtained under different circumstances, such as zero division or counter intuitive cases; in contrast, the proposed similarity measure successfully overcomes this weakness.
Fuzzy Math
Aifang Xie; Zhang Qieqiong
Volume 21, Issue 2 , March and April 2024, Pages 105-116
Abstract
In literature, for the four common classes of uninorms, the modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the modularity equation involving two uninorms with continuous underlying functions.We discuss this modularity ...
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In literature, for the four common classes of uninorms, the modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the modularity equation involving two uninorms with continuous underlying functions.We discuss this modularity equation in detail by dividing the main section into two parts. The structure characterization of the two uninorms is almost completely obtained and it is found that they are equal in the unit square except in a subdomain.
Fuzzy Math
Mengying Liu; Yueli Yue
Volume 21, Issue 2 , March and April 2024, Pages 117-127
Abstract
In this paper, for each commutative and integral quantale, we give the stratified Sierpinski $L$-algebraic closure space and a sobrification of stratified $L$-algebraic closure spaces. Furthermore, we show that $\bf{S}$$L$-$\bf{AC}_0$---the category of stratified $S_0$-$L$-algebraic closure spaces is ...
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In this paper, for each commutative and integral quantale, we give the stratified Sierpinski $L$-algebraic closure space and a sobrification of stratified $L$-algebraic closure spaces. Furthermore, we show that $\bf{S}$$L$-$\bf{AC}_0$---the category of stratified $S_0$-$L$-algebraic closure spaces is epireflective in $\bf{S}$$L$-$\bf{AC}$---the category of stratified $L$-algebraic closure spaces, and $\bf{Sob}$$L$-$\bf{AC}$---the category of sober $L$-algebraic closure spaces is epireflective and $\mathcal{E}$-firm epireflective in the category $\bf{S}$$L$-$\bf{AC}_0$.
Fuzzy modelling
Lang Mao; Yang Y Yong
Volume 21, Issue 2 , March and April 2024, Pages 129-140
Abstract
For a class of uncertainty abstract economies in fuzzy environment (UASIFEs), we establish for each UASIFE, the existenceof fuzzy strong Berge equilibrium by the Kakutani-Fan Glicksberg fixed point theorem. Moreover, we investigatethe stability of equilibrium, and prove that most UASIFEs are essential ...
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For a class of uncertainty abstract economies in fuzzy environment (UASIFEs), we establish for each UASIFE, the existenceof fuzzy strong Berge equilibrium by the Kakutani-Fan Glicksberg fixed point theorem. Moreover, we investigatethe stability of equilibrium, and prove that most UASIFEs are essential and each UASIFE has at least an essentialcomponent by Fort theorem and reduction to absurdity, respectively.
Computer Science
Lakshmi Srinivasulu Dandugala; Koneru Suvarna Vani
Volume 21, Issue 2 , March and April 2024, Pages 141-160
Abstract
The act of gathering, looking over, and analyzing a lot of data to find patterns, insights, and market trends that canhelp businesses make more effective choices is known as big data analysis (BDA). Quick and effective access to thisdata allows businesses to be flexible in developing strategies to hold ...
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The act of gathering, looking over, and analyzing a lot of data to find patterns, insights, and market trends that canhelp businesses make more effective choices is known as big data analysis (BDA). Quick and effective access to thisdata allows businesses to be flexible in developing strategies to hold onto their competitive edge. To analyze massiveamounts of data quickly through parallel processing, the structure of the Hadoop software employs the MapReducemethodology. Computational solid resources are necessary for BDA, although they are not always available. Developingnew clustering techniques that could handle this kind of data processing became crucial. Therefore, in this research,we presented a novel, effective fuzzy-based Improved Multiview Fuzzy C-Means Algorithm (IMV-FCA) to boost theclustering strategy. To summarize, fuzzy-based IMV-FCA clustering presents the ensemble of the MobileNet V2 model,and three-layered stacked Bidirectional LSTM (MVSBiLSTM) to increase computing speed and effectiveness. It alsopresents a function that calculates the separation among the cluster center and the particular instance, to assist withbetter clustering. By simulating shared memory space and parallelizing on the framework known as MapReduce onthe Hadoop cloud computing platform, the distributed database is utilized to improve the method’s effectiveness whilereducing its time complexities. The experimental investigation was conducted on existing approaches, and the proposedapproach was analyzed using three standard datasets. While differentiating from existing approaches, the presentedapproach yields greater performances in terms of various metrics.
Optimization
Mehrdad Rasoulzadeh; Seyyed Ahmad Edalatpanah; Mohammad Fallah; Seyyed Esmaeil Najafi
Volume 21, Issue 2 , March and April 2024, Pages 161-179
Abstract
In the dynamic world of financial investment, crafting an optimal stock portfolio that judiciously balances risk, return, and efficiency emerges as a critical challenge. Despite the wealth of research on financial portfolio optimization, prevailing methodologies predominantly emphasize either risk minimization ...
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In the dynamic world of financial investment, crafting an optimal stock portfolio that judiciously balances risk, return, and efficiency emerges as a critical challenge. Despite the wealth of research on financial portfolio optimization, prevailing methodologies predominantly emphasize either risk minimization or return maximization, often overlooking the imperative for a holistic strategy that simultaneously boosts efficiency and effectiveness. Addressing this gap in the literature, this study introduces an innovative four-objective model that intricately blends risk, return, and efficiency considerations for the strategic selection of stock portfolios. This model ingeniously integrates the foundational principles of Markowitz's mean-variance analysis with the sophisticated network data envelopment analysis (NDEA) techniques, significantly refining the portfolio selection methodology. It further distinguishes itself by incorporating returns represented as trapezoidal intuitionistic fuzzy numbers, adeptly capturing the inherent uncertainties in financial returns. Additionally, the model employs the network data envelopment analysis's cross-efficiency principle, providing a nuanced measure of company performance. To effectively navigate the complexities of this model, we deploy the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a multi-objective genetic algorithm, demonstrating the model's capability to unearth optimal solutions efficiently. The comparative analysis highlights that the proposed model significantly outperforms the efficiency and effectiveness of existing models, marking a substantial advancement in portfolio optimization strategies.
Approximate Reasoning
Zu ming Peng; Xian min Zhang
Volume 21, Issue 2 , March and April 2024, Pages 181-200
Abstract
The generalized hypothetical syllogism (GHS) is an important property of fuzzy implications for its applications in approximate reasoning. Due to the complexity of the (GHS) and the variety of fuzzy implications, in this work, we study the (GHS) property with respect to a strict t-norm T for fuzzy implications ...
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The generalized hypothetical syllogism (GHS) is an important property of fuzzy implications for its applications in approximate reasoning. Due to the complexity of the (GHS) and the variety of fuzzy implications, in this work, we study the (GHS) property with respect to a strict t-norm T for fuzzy implications which come from some well known families of fuzzy implications, viz., (S, N)-, QL-, g-, (U, N)-, (T, N)-implications. First, some results on the (GHS) for fuzzy implications are presented. Second, the (GHS) property of (S, N)-, QL-, g-, (U, N)-, and (T, N)-implications is studied. Finally, the (GHS) property for the fuzzy implications generated from old ones using the method of sup-T composition is also studied.
