Three-Way Fuzzy Sets and Their Applications (II)

Wang, Jingqian; Zhang, Xiaohong; Hu, Qingqing

doi:10.3390/axioms11100532

Cited by 15 publications

(4 citation statements)

References 42 publications

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“…Hence, in the future, the research content of this paper will be applied to some practical data (such as multi-modal data). Furthermore, logical operators [50] and three-way decision making [51,52] will be connected with the research content of this paper in further research.…”

Section: Discussionmentioning

confidence: 97%

Choquet-like Integrals with Multi-Neighborhood Approximation Numbers for Novel Covering Granular Reduction Methods

Wang,

Shao,

Zhang

2023

Mathematics

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Covering granular reduction is an important issue in multi-covering information systems. The main methods to solve this problem are set operators. How to solve this problem by quantitative analysis is an interesting topic. Furthermore, as a type of nonlinear fuzzy aggregation function (which is a quantitative tool), Choquet-like integrals with fuzzy measures are widely used in many files. However, the corresponding fuzzy measures in Choquet-like integrals are given by man, not by data. In this work, we present two types of multi-neighborhood approximation numbers in multi-covering information systems, which are used to establish Choquet-like integrals. Furthermore, they are applied to deal with the problem of granular reduction in multi-covering information systems. First, the notions of lower and upper multi-neighborhood approximation numbers are presented in a multi-covering information system, as well as their properties. Furthermore, some conditions under which multi-covering information systems induce the same lower and upper multi-neighborhood approximation numbers are presented. Second, two covering granular reduction methods based on multi-neighborhood approximation numbers are presented in multi-covering information systems. Third, multi-neighborhood approximation numbers are used to establish Choquet-like integrals, which are applied in covering granular reduction. Finally, these methods are compared with existing methods through experiments, which are used to demonstrate the effectiveness and benefits of our methods.

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Section: Discussionmentioning

confidence: 97%

Choquet-like Integrals with Multi-Neighborhood Approximation Numbers for Novel Covering Granular Reduction Methods

Wang,

Shao,

Zhang

2023

Mathematics

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“…Other multigranulation fuzzy covering rough set models (such as [34][35][36]) can also be represented by matrices in the future. On the contrary, the recent generalized types of fuzzy sets: (i) (2, 1)-Fuzzy sets: properties, weighted aggregated operators, and their applications to multicriteria decision-making methods [38]; (ii) new generalization of fuzzy soft sets: (a, b)-fuzzy soft sets [39]; (iii) three-way fuzzy sets [40] will be connected with the research content of this paper in further research.…”

Section: Discussionmentioning

confidence: 99%

Matrix Approaches for Covering-Based Multigranulation Fuzzy Rough Set Models

Chang¹,

Jun-chao²

2023

Journal of Mathematics

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Multigranulation rough set theory is one of the most effective tools for data analysis and mining in multicriteria information systems. Six types of covering-based multigranulation fuzzy rough set (CMFRS) models have been constructed through fuzzy β -neighborhoods or multigranulation fuzzy measures. However, it is often time-consuming to compute these CMFRS models with a large fuzzy covering using set representation approaches. Hence, presenting novel methods to compute them quickly is our motivation for this paper. In this article, we study the matrix representations of CMFRS models to save time in data processing. Firstly, some new matrices and matrix operations are proposed. Then, matrix representations of optimistic CMFRSs are presented. Moreover, matrix approaches for computing pessimistic CMFRSs are also proposed. Finally, some experiments are proposed to illustrate the effectiveness of our approaches.

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“…In addition, considering non-commutative fuzzy logic, the non-commutative generalization of weak IBL-algebras is also worth studying, which is what we are doing. Moreover, as an interesting research topic, we can consider a new model of fuzzy rough sets (see [26][27][28]) based on inflationary (pseudo-) general residuated lattices.…”

Section: Discussionmentioning

confidence: 99%

Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

Zhang

Liang²,

Bedregal³

2022

Mathematics

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After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every inflationary general overlap function can induce an inflationary BL-algebra by a counterexample and thus propose the new concept of weak inflationary BL-algebras. We prove that each inflationary general overlap function corresponds to a weak inflationary BL-algebra; therefore, two mistaken results in the previous paper are revised. In addition, some properties satisfied by weak inflationary BL-algebras are discussed, and the relationships among some non-classical logic algebras are analyzed. Finally, we establish the theory of filters and quotient algebras of inflationary general residuated lattice (IGRL) and inflationary pseudo-general residuated lattice (IPGRL), and characterize the properties of some kinds of IGRLs and IPGRLs by naBL-filters, (weak) inflationary BL-filters, and weak inflationary pseudo-BL-filters.

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Three-Way Fuzzy Sets and Their Applications (II)

Cited by 15 publications

References 42 publications

Choquet-like Integrals with Multi-Neighborhood Approximation Numbers for Novel Covering Granular Reduction Methods

Choquet-like Integrals with Multi-Neighborhood Approximation Numbers for Novel Covering Granular Reduction Methods

Matrix Approaches for Covering-Based Multigranulation Fuzzy Rough Set Models

Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

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