Fuzzy Transforms for Hesitant, Soft or Intuitionistic Fuzzy Sets

Močkoř, Jǐŕı

doi:10.1007/s44196-021-00018-9

Cited by 3 publications

(1 citation statement)

References 54 publications

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“…Information fusion theories and methods [1][2][3][4][5][6] are powerful tools in numerous applications including management decision-making and evaluations [7][8][9][24][25][26][27][28][29][30][31]. For a collection of n input values, which are often expressed by a vector, a commonly used aggregation operator can merge those n inputs into a single output in some strict and standard manners.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Rules-Based and Preferences Induced Weights Allocation in Group Decision-Making with BUI

Yager

Zhang

et al. 2022

Int J Comput Intell Syst

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Decision-makers’ subjective preferences can be well modeled using preference aggregation operators and related induced weights allocation mechanisms. However, when several different types of preferences occur in some decision environment with more complex uncertainties, repeated uses of preferences induced weights allocation sometimes become unsuitable or less reasonable. In this work, we discuss a common decision environment where several invited experts will offer their respective evaluation values for a certain object. There are three types of preferences which will significantly affect the weights allocations from experts. Instead of unsuitably performing preference induced weights allocation three times independently and then merging the results together using convex combination as some literatures recently did, in this work, we propose some organic and comprehensive rules-based screen method to first rule out some unqualified experts and then take preference induced weights allocation for the refined group of experts. A numerical example in business management and decision-making is presented to show the cognitive reasonability and practical feasibility.

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Section: Introductionmentioning

confidence: 99%

Comprehensive Rules-Based and Preferences Induced Weights Allocation in Group Decision-Making with BUI

Yager

Zhang

et al. 2022

Int J Comput Intell Syst

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The Fuzzy Natural Transformations, the Algebra P(ω)/fin and Generalized Encoding Theory

Jobczyk

2022

IEEE Access

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A category theory constitutes a convenient conceptual apparatus to organize the worlds of mathematical entities. The concept of fuzzy natural transformation as an abstract mapping on functors is one of the essential concepts of this theory. If we admit a piece of non-commutativity in its definition diagrams, then the 'upward' and the 'downward' diagram parts generate different result sets. In this way, we can introduce the concept of fuzzy natural transformation. We deal with the multi-fuzzy natural transformation if such a transformation is based on a multi-diagram. This paper aims to describe the multi-fuzzy natural transformation situation when the symmetric difference of the result is finite. It allows us to organize the whole spectrum of the result sets in a unique quotient algebra P comp (ω)/fin. Different algebraic properties of this structure will be explored, and a piece of classical encoding theory will be reconstructed in the environment determined by this algebra. In particular, the concepts of the k-multi similarity, the abstract k-multi similarity, the k-similarity balls, and the abstract k-similarity balls are introduced as some generalization of the idea of Hamming's distances and Hamming's balls. Finally, it is shown how to automate some verification processes in this context using an R-based programming environment.

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Semiring-Valued Fuzzy Sets and F-Transform

Močkoř

2021

Mathematics

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The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard MV-algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of MV-algebra-valued fuzzy type structures to semiring-valued fuzzy sets, the F-transforms for these fuzzy type structures is introduced. The advantage of this procedure is, among other things, that the properties of this F-transform are analogous to the properties of the classical F-transform and because these properties are proven for any semiring-valued fuzzy sets, it is not necessary to prove them for individual fuzzy type structures.

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Fuzzy Transforms for Hesitant, Soft or Intuitionistic Fuzzy Sets

Cited by 3 publications

References 54 publications

Comprehensive Rules-Based and Preferences Induced Weights Allocation in Group Decision-Making with BUI

Comprehensive Rules-Based and Preferences Induced Weights Allocation in Group Decision-Making with BUI

The Fuzzy Natural Transformations, the Algebra P(ω)/fin and Generalized Encoding Theory

Semiring-Valued Fuzzy Sets and F-Transform

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