A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application

Garg, Harish; Kumar, Kamal

doi:10.24200/sci.2017.4454

Cited by 23 publications

(29 citation statements)

References 45 publications

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“…In the future, we will apply the proposed operators ♢, , ♠, ♣, , →, $ in other fuzzy environment [26,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Table 1 The results of ♠, →, $, ♣, operations on P and Q Operations Results Table 4 The tabular form of interval-valued Pythagorean fuzzy decision matrix in Example 5.…”

Section: Discussionmentioning

confidence: 99%

New Operations for Interval-valued Pythagorean Fuzzy Set

Peng¹

2018

Scientia Iranica

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Interval-valued Pythagorean fuzzy set (IVPFS), originally proposed by Peng and Yang, is a novel tool to deal with vagueness and incertitude. As a generalized set, IVPFS has close relationship with interval-valued intuitionistic fuzzy set (IV-IFS). IVPFS can be reduced to IVIFS satisfying the condition µ + + ν + ≤ 1. However, the related operations of IVPFS do not take different conditions into consideration. In this paper, we initiate some new interval-valued Pythagorean fuzzy operators (♢, , ♠, ♣, , →, $) and discuss their properties in relation with some existing operators (∪, ∩, ⊕, ⊗) in detail. It will promote the development of interval-valued Pythagorean fuzzy operators. Later, we propose an algorithm to deal with multi-criteria decision making (MCDM) problem based on proposed ♠ operator. Finally, the effectiveness and feasibility of proposed algorithm is demonstrated by mine emergency decision making example.

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Section: Discussionmentioning

confidence: 99%

New Operations for Interval-valued Pythagorean Fuzzy Set

Peng¹

2018

Scientia Iranica

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“…Many math models such as network analysis, 48–51 risk and reliability analysis, 52–54 visible graph, 55 and fuzzy sets 56–60 . IFS is an extension of the classical fuzzy sets, which has been used in a wide scope of application 61–65 . It considers three degrees simultaneously, which is more flexible, practical, and efficient than classical FS in dealing with ambiguity and uncertainty.…”

Section: Preliminariesmentioning

confidence: 99%

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Xue

Deng

2020

Int J Intell Syst

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Entailment for measure-based belief structures can extend the possible probability value range of variables on a space and obtain more information from variables. However, if the variable space comes from intuitionistic fuzzy sets, the classical entailment for measure-based belief structures will not work in this issue. To deal with this situation, we propose the entailment for intuitionistic fuzzy sets based on generalized belief structures in this paper to apply the entailment for measure based belief structures on space, which is made up of non-membership degree, membership degree and hesitancy degree of a given intuitionistic fuzzy sets. Numerical examples are mentioned to prove the effectively and flexibility of this proposed entailment model. The experimental results indicate that the proposed algorithm can extend the possible probability value range of variables of space efficiently and obtain more information from intuitionistic fuzzy sets.belief function, Dempster-Shafer evidence theory, entailment, generalized belief structures, intuitionistic fuzzy sets | INTRODUCTIONIn real life, there are a lot of uncertainties in the real world. To address the uncertainties, many mathematical theories are proposed, such as probability theory, 1 fuzzy sets (FS), 2 Dempster-Shafer evidence theory, 3,4 intuitionistic fuzzy sets (IFS), 5,6 information quality, 7-11 Z-number, 12 fuzzy reasoning, 13-15 D-number, 16-18 entropy function, [19][20][21][22] and belief structure. 23,24 Among these theories and models, the IFS 25 considering the degree of hesitancy, membership, and nonmembership of objects, can deal with the uncertainties more flexibly and accurately, which has been used in many fields widely, 26 such as the uncertainty decision making, 27,28 pattern recognition 29 and so on.Recently, Yager proposed the entailment for measure based belief structures with a space, which has the promising aspect. 30 However, what the entailment for measure-based belief structures for a given IFS is still an open issue to be addressed. This paper proposes entailment for intuitionistic fuzzy sets based on generalized belief structures, which treats hesitancy degree, non-membership degree and membership degree of a given intuitionistic fuzzy set as three variables in a space X . Assume V takes its value in the X and is an uncertain variable. If g 1 and g 2 be two generalized belief structures on X and g 2 contains g 1 , then the belief of the statement that V is true based on g 2 will be smaller than that of the statement that V is true based on g 1 and the plausibility of the statement that V is true based on g 2 will be bigger than that of the statement that V is true based on g 1 .The remain of this paper is structured as follows. Section 2 introduces the preliminary. Section 3 presents the entailment for intuitionistic fuzzy sets based on generalized belief structures. Section 4 illustrates the flexibility and accuracy of the entailment for intuitionistic fuzzy sets based on generalized belief structures. Section 5 summarizes the...

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“…These mathematical techniques were adapted for decision making based the fuzzy set and its some extensions [20][21][22][23][24][25][26]. In addition to the fuzzy modelling of TOPSIS, ELECETRE and etc., many algorithmic solutions were proposed for decision making under fuzzy environment [27][28][29][30][31]. In 2002, Maji et al [32] put forward that the soft sets can be used to solve decision making problems involving parametric data based on two-valued logic.…”

Section: Introductionmentioning

confidence: 99%

Three-valued soft set and its multi-criteria group decision making via TOPSIS and ELECTRE

Akçetin

Kamacı²

2020

Scientia Iranica

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The purpose of this paper is to introduce a generalization of Molodtsov's approach to soft sets obtained by passing from the classical two-valued logic underlying those sets to a three-valued logic, where the third truth value can usually be interpreted as either non-determined (i.e., between true and false) or unknown. This extension of soft set approach allows for more intuitive and clearer representation of various decision making problems involving incomplete or uncertain information. In other words, it is a useful way to analyze soft set based multi-criteria group decision making problems under the lack of information resulting from the inability to determine the data. In this paper, we introduce the concept of three-valued soft set and its some operations and products. We propose the formulas to calculate all possible choice values for each object in the (weighted) three-valued soft sets, and thus calculate their respective decision values. By modifying the TOPSIS and ELECTRE methods to deal with multi-criteria group decision problems, three-valued soft set based decision making algorithms are constructed. To demonstrate the practicality of these algorithms, we address the examples adapted from the decision problems in real-life. Lastly, some aspects of the efficiency of the proposed algorithms are discussed with computational experiments.

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A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application

Cited by 23 publications

References 45 publications

New Operations for Interval-valued Pythagorean Fuzzy Set

New Operations for Interval-valued Pythagorean Fuzzy Set

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Three-valued soft set and its multi-criteria group decision making via TOPSIS and ELECTRE

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