# Iranian journal of fuzzy systems Volume:20 Issue: 7, Nov-Dec 2023

• تاریخ انتشار: 1402/09/15
• تعداد عناوین: 11
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• J. Gao, Z. S. Xu *, Y. S. Mao Pages 1-26
The generalized interval-valued orthopair fuzzy sets provide an extension of Yager’s generalized orthopair fuzzy sets, where membership and non-membership degrees are subsets of closed interval [0, 1]. Due to the uncertainty and ambiguity of real life, it is more superior for decision makers to provide their judgments by intervals rather than crisp numbers. Moreover, in the era of huge scale and rapid updating of information, individual weights have been quietly diluted, and the integration of information one by one is time-consuming and complicated. In recent years, some  cholars have conducted research on the calculus of generalized orthopair fuzzy sets, but no research has further revealed the intrinsic connection between the integrals of generalized interval-valued orthopair fuzzy sets and traditional aggregation operators, which is very important in applications such as large group decision making. In order to fill this theoretical gap, this paper aims to study the integrals of generalized interval-valued orthopair fuzzy functions. In detail, we define the indefinite integral starting from the inverse operations of the interval-valued q-rung orthopair fuzzy functions  (IVq-ROFFs)’ derivatives, and some fundamental properties with rigorous mathematical proofs are also discussed. To be more  practical, we continue to develop definite integrals for both simplified and generalized IVq-ROFFs. Besides, we give the corresponding Newton-Leibniz formula through limit procedure, which shows the calculation relationship between the  indefinite and definite integrals of the IVq-ROFFs. After obtaining the basic calculus results under generalized interval-valued orthopair fuzzy circumstance, we further reveal the inherent link between the integrals of generalized IVq-ROFFs and the traditional discrete aggregation operators. Finally, the practicability and feasibility of the proposed definite  integral models are illustrated by an example of public health emergency group decision-making, and sensitivity analysis and comparison are also carried out.
Keywords: Fuzzy sets, Decision making, Aggregation operators, Information fusion
• S. Rezaei Aderyani, R. Saadati, T. Allahviranloo, S. Abbasbandy *, M. Catak Pages 27-36
Our aim in this paper is to study the fuzzy stability of a fractional Lorenz system in the sense of the Caputo-Fabrizio derivative and a fractional financial crisis in the sense of }−Hilfer derivative. Defining a new type of fuzzy control function that has a dynamic situation helps us to investigate new stability results for these mathematical models.
Keywords: Fractional Lorenz system, stability, Caputo-Fabrizio derivative, fractional financial crisis, Fuzzy sets
• K. Atanassov *, R. Tsvetkov Pages 37-53
Two new intuitionistic fuzzy operations (union and intersection) are defined. Based on them, two new topological operators (of a closure and of an interior types) are introduced. Some properties of these obects are studied. Based on them, four new intuitionistic fuzzy topological structures are introduced and some of their properties are discussed. Integral forms of both new intuitionistic fuzzy operations and of both intuitionistic fuzzy operators are given.
Keywords: Intuitionistic fuzzy operation, intuitionistic fuzzy operator, Intuitionistic fuzzy set, intuitionistic fuzzy topological structure
• M. B. Dowlatshahi *, A. Hashemi Pages 55-70
Feature selection (FS) has shown remarkable performance in decreasing the dimensionality of high-dimensional datasets by selecting a good subset of features. Labeling high-dimensional data can be expensive and time-consuming as labeled samples are not always available. Therefore, providing effective unsupervised FS methods is essential in machine learning. This article provides a fuzzy multi-criteria decision-making method for unsupervised FS in which an ensemble of unsupervised FS rankers is utilized to evaluate the features. These methods are aggregated based on a fuzzy TOPSIS method. This is the first time a fuzzy multi-criteria decision-making approach has been used for an FS problem. Multiple comparisons are made to show the optimality and effectiveness of the proposed strategy against multiple competing FS methods. Our approach regarding two classification metrics, F-score and accuracy, appears superior to comparable  strategies. Also, it is performing so swiftly.
Keywords: Unsupervised feature selection, fuzzy TOPSIS, fuzzy multi-criteria decision-making, high-dimensional data, ensemble of feature selection methods
• G. Jager * Pages 71-84
In the category of ⊤-quasi-Cauchy spaces, completeness and completion can be studied in a non-symmetric framework encompassing ⊤-quasi-uniform (limit) spaces. Based on constructions by E.E. Reed in the category of Cauchy spaces and, recently, by L. Reid and G. Richardson in the category of ⊤-Cauchy spaces, we give a family of completions for a non-complete ⊤-quasi Cauchy space. As particular instances we study pretopological and topological completions of ⊤-quasi-Cauchy spaces.
Keywords: fuzzy topology, pair ⊤-filter, Cauchy pair ⊤-filter, ⊤-quasi-Cauchy space, ⊤-quasi-uniform space, ⊤-quasi uniform limit space, L-metric space
• I. Kaya *, S. Yalcin Pages 85-99
Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (µ) and variance (σ2) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and  sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more  broadly more flexibility. For this aim, the main parameters of PCIs have been defined  and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as Csp, Cspk, Cfp and Cfpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic,  more sensitive, and more comprehensive results.
Keywords: Process capability analysis, Process capability indices, the fuzzy set theory, Pythagorean fuzzy sets
• F. G. Shi * Pages 101-109
In this paper, our aim is to present some characterizations of M-fuzzifying convex matroids. First we discuss the relation between M-fuzzifying convex matroids and M-fuzzy families of dependent sets. Secondly, we give characterizations of M-fuzzifying convex matroids by M-fuzzifying rank functions. Finally we discuss the relation between two concept of M-fuzzifying hull (closure) operators.
Keywords: M-fuzzifying convex matroid, M-fuzzifying hull operator, M-fuzzy family of dependent sets, M-fuzzifying circuit map, M-fuzzifying rank function
• G. D. C¸Aylı *, R. Mesiar Pages 111-126
In this article, we go on to discuss the structure of uninorms on bounded lattices. We suggest two techniques to yield  uninorms with some constraints on the identity element by applying that the t-norms and t-conorms are always present on the considered bounded lattices. These techniques ensure new approaches for getting idempotent uninorms on bounded lattices when regarding infimum t-norm and supremum t-conorm. Furthermore, we display the distinctness between our new construction techniques and the published ones.
Keywords: Bounded lattice, idempotent uninorm, t-norm, t-conorm, uninorm
• R. A. Borzooei *, M. Aaly Kologani, G. R. Rezaei Pages 127-143
In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology.
Keywords: Hoop, maximal filter, prime filter, radical, r-filter, p-filter
• S. Motamed, J. Moghaderi, A. Borumand Saeid * Pages 145-155
In this article, with the aim of further investigating BL-algebras, the concepts of Unity Co-annihilator-filters (UC-filters) is introduced and discussed. Also, for the faster study of UC-filters in BL-algebras, some equivalent conditions are obtained, and (with some examples) it is shown that these filters have differences. In addition, we consider several additional  conditions imposed on UC-filters and prime filters and establish links between them. So, we get relationships between  these types of filters and prime filters in BL-algebras. Finally, the form of all UC-saturated ∨-closed subsets of a G- algebras (by the concept of UC-saturated ∨-closed subsets) is stated.
Keywords: BL-algebra, (UC, prime)-filter, unity co-annihilator elements
• M. Joghataee, T. Allahviranloo *, F. Hosseinzadeh Lotfi, A. Ebrahimnejad, S. Abbasbandy, A. Amirteimoori, M. Catak Pages 157-174
Generally exploring the exact solution of linear programming problems in which all variables and parameters are  Z-numbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an  important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such  problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness  of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed  method have been compared with some existing methods.
Keywords: Z-numbers, linear programming problem (LPP), Ranking function