New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

Bo, Chunxin; Zhang, Xiao­hong

doi:10.3390/sym9110268

Cited by 37 publications

(20 citation statements)

References 37 publications

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“…This allows aggregation functions (as studied on the unit interval I in, e.g., [46,47,[76][77][78]) to be introduced on (D * , ≤ D * ). Observe also that the lattice (D * , ≤ D * ) was considered in recent applications of picture fuzzy sets [103,104].…”

Section: Generalizations To Higher Dimensionsmentioning

confidence: 99%

L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

Klement

Mesiar

2018

Mathematics

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We review several generalizations of the concept of fuzzy sets with two- or three-dimensional lattices of truth values and study their relationship. It turns out that, in the two-dimensional case, several of the lattices of truth values considered here are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy set. Finally we also discuss some questionable notations, in particular, those of “intuitionistic” and “Pythagorean” fuzzy sets.

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Section: Generalizations To Higher Dimensionsmentioning

confidence: 99%

L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

Klement

Mesiar

2018

Mathematics

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“…Peng et al [26] proposed an PFS algorithm and tested it in decision-making. Bo and Zhang [27] studied some new operations of picture fuzzy relations such as type-2 inclusion relation, type-2 union, type-2 intersection and type-2 complement operations and also defined the anti-reflexive kernel, symmetric kernel, reflexive closure and symmetric closure of a picture fuzzy relation. For more detailed study, we refer to [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Linguistic Picture Fuzzy Dombi Aggregation Operators and Their Application in Multiple Attribute Group Decision Making Problem

et al. 2019

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The aims of this study are to propose the linguistic picture fuzzy Dombi (LPFD) aggregation operators and decision-making approach to deal with uncertainties in the form of linguistic picture fuzzy sets. LPFD operators have more flexibility due to the general fuzzy set. Utilizing the Dombi operational rule, the series of Dombi aggregation operators were proposed, namely linguistic picture fuzzy Dombi arithmetic/geometric, ordered arithmetic/ordered geometric and Hybrid arithmetic/Hybrid geometric aggregation operators. The distinguished feature of these proposed operators is studied. At that point, we have used these Dombi operators to design a model to deal with multiple attribute decision-making (MADM) issues under linguistic picture fuzzy information. Finally, an illustrative example to evaluate the emerging technology enterprises is provided to demonstrate the effectiveness of the proposed approach, together with a sensitivity analysis and comparison analysis, proving that its results are feasible and credible.

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“…Yang et al [12] extended the notion of picture fuzzy soft set. Other decision making procedures in the picture fuzzy set can be retrieved in [13,14,15,16,17,18,19,20,21,22]. Wei [23] summarized some similarity measures in the picture fuzzy set.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of Picture Fuzzy Clustering: Convergence and Property

Phuong

Thong²,

Sơn³

2018

JCC

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Recently, picture fuzzy clustering (FC-PFS) has been introduced as a new computational intelligence tool for various problems in knowledge discovery and pattern recognition. However, an important question that was lacked in the related researches is examination of mathematical properties behind the picture fuzzy clustering algorithm such as the convergence, the boundary or the convergence rate, etc. In this paper, we will prove that FC-PFS converges to at least one local minimum. The similarities and differences between this algorithm and other clustering methods are compared. Analysis on the loss function is also considered.

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New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

Cited by 37 publications

References 37 publications

L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

Linguistic Picture Fuzzy Dombi Aggregation Operators and Their Application in Multiple Attribute Group Decision Making Problem

Theoretical Analysis of Picture Fuzzy Clustering: Convergence and Property

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