Picture inference system: a new fuzzy inference system on picture fuzzy set

Sơn, Lê Hoàng; Viet, Pham Van; Hai, Pham Van

doi:10.1007/s10489-016-0856-1

Cited by 124 publications

(32 citation statements)

References 30 publications

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“…The new basic connectives in picture fuzzy logic on PFS firstly were presented in [11,25]. These new concepts are supporting to new computing procedures in computational intelligence problems and in other applications (see [17,18,19,20,21,22,23,24]).…”

Section: Introductionmentioning

confidence: 99%

Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Cường

2019

JCC

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Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟intuitionistic fuzzy set. The new concept could be useful for many computational intelligentproblems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].Newconcept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with theYager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notionson PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy softset. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picturenegation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.As aresult we will have a new branch of the picture fuzzy set theory.

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Section: Introductionmentioning

confidence: 99%

Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Cường

2019

JCC

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“…Nguyen et al [14] use picture fuzzy sets to applied for Geographic Data Clustering. Van Dinh et al [18] introduce the picture fuzzy set database. Cuong and Hai [3] studied some fuzzy logic operators for picture fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

Some Measures of Picture Fuzzy Sets and Their Application in Multi-attribute Decision Making

Định¹,

Thảo²

2018

IJMSC

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To measure the difference of two fuzzy sets / intuitionistic sets, we can use the distance measure and dissimilarity measure between fuzzy sets. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide the formulas for determining these values. We also present an application of dissimilarity measures in multi-attribute decision making.Index Terms: Picture fuzzy set (PFS), difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, multi-attribute decision making.

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“…Picture fuzzy sets give three degrees of an element named degree of positive membership, degree of neutral membership and degree of negative membership, respectively. The picture fuzzy set solved the voting problem successfully, and is applied to clustering [31], fuzzy inference [32], and decision-making [33,34].…”

Section: Introductionmentioning

confidence: 99%

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

Zhang

2017

Symmetry

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Abstract:In this paper, some new operations and basic properties of picture fuzzy relations are intensively studied. First, a new inclusion relation (called type-2 inclusion relation) of picture fuzzy relations is introduced, as well as the corresponding type-2 union, type-2 intersection and type-2 complement operations. Second, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure and symmetric closure of a picture fuzzy relation are introduced and their properties are explored. Moreover, a new method to solve picture fuzzy comprehensive evaluation problems is proposed by defining the new composition operation of picture fuzzy relations, and the picture fuzzy comprehensive evaluation model is built. Finally, an application example (about investment risk) of picture fuzzy comprehensive evaluation is given, and the effective experiment results are obtained.

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Picture inference system: a new fuzzy inference system on picture fuzzy set

Cited by 124 publications

References 30 publications

Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Some Measures of Picture Fuzzy Sets and Their Application in Multi-attribute Decision Making

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

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