Interval-Valued Pseudo Overlap Functions and Application

Liang, Rong; Zhang, Xiao­hong

doi:10.3390/axioms11050216

Cited by 17 publications

(9 citation statements)

References 38 publications

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“…Therefore, POFs and PGFs have a wide adaptability and application value. There are still many theoretical and applied problems to be studied in terms of pseudo overlap functions and fuzzy logic (see [42][43][44][45][46][47]).…”

Section: Discussionmentioning

confidence: 99%

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Zhang

Liang

Bustince

et al. 2022

Axioms

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Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.

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Section: Discussionmentioning

confidence: 99%

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Zhang

Liang

Bustince

et al. 2022

Axioms

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“…In the future, we will continue to study partial residuated lattices and their special subclasses, and reveal the internal relationship between partial residuated lattices (regular partial residuated lattices) and other logical algebras [21][22][23]. In addition, we will study fuzzy reasoning and fuzzy rough sets based on partial residuated lattices, as well as other applications [24][25][26].…”

Section: Discussionmentioning

confidence: 99%

Regular Partial Residuated Lattices and Their Filters

Sheng

Zhang

2022

Mathematics

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To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices.

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“…These functions have been studied in terms of their related properties and applications. Furthermore, Liang and Zhang [10,22] have generalized the notion of interval-valued and n-dimensional pseudooverlap functions.…”

Section: Definition 3 ([6]) a Mapping Gmentioning

confidence: 99%

Some Construction Methods for Pseudo-Overlaps and Pseudo-Groupings and Their Application in Group Decision Making

García-Zamora

Paiva

Cruz

et al. 2023

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In many real-world scenarios, the importance of different factors may vary, making commutativity an unreasonable assumption for aggregation functions, such as overlaps or groupings. To address this issue, researchers have introduced pseudo-overlaps and pseudo-groupings as their corresponding non-commutative generalizations. In this paper, we explore various construction methods for obtaining pseudo-overlaps and pseudo-groupings using overlaps, groupings, fuzzy negations, convex sums, and Riemannian integration. We then show the applicability of these construction methods in a multi-criteria group decision-making problem, where the importance of both the considered criteria and the experts vary. Our results highlight the usefulness of pseudo-overlaps and pseudo-groupings as a non-commutative alternative to overlaps and groupings.

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Interval-Valued Pseudo Overlap Functions and Application

Cited by 17 publications

References 38 publications

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Regular Partial Residuated Lattices and Their Filters

Some Construction Methods for Pseudo-Overlaps and Pseudo-Groupings and Their Application in Group Decision Making

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