A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers

Nan, Jiang-Xia; Li, Dengfeng; Zhang, Maojun

doi:10.1080/18756891.2010.9727699

Cited by 85 publications

(52 citation statements)

References 26 publications

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“…In this subsection, analogous to the idea of Nan et al [20], the mean value index of a TIFN is de ned as follows.…”

Section: A New Value Index Of Tifns and Ranking Methods 31 The Mean mentioning

confidence: 99%

“…A number of achievements on TIFNs have been proposed. Roughly, these achievements may be divided into two types: ranking methods of TIFNs and their applications to decision making problems [13][14][15][16][17][18][19][20][21] and aggregation operators of TIFNs and their applications to decision making problems [22][23][24][25][26][27], which are brie y reviewed in the following, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the possibility method, Wan and Dong [19] developed a method for MAGDM based on TIFNs with incomplete preference information. In addition to other methods, Nan et al [20] investigated the ranking order relations of TIFNs, which are applied to matrix games with payo s of TIFNs.…”

Section: Introductionmentioning

confidence: 99%

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A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

Wan

Xu²

2017

Scientia Iranica

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Abstract. The trustworthy service selection is a typical Multi-Attribute Group DecisionMaking (MAGDM) problem. The aim of this paper is to develop a novel method for MAGDM with Triangular Intuitionistic Fuzzy Numbers (TIFNs) and apply it to the trustworthy service selection problem. Firstly, we de ne the mean-index, variance-index, and standard deviation of TIFN. Moreover, a new distance measure of TIFNs is proposed, and the corresponding proofs are given. Based on these concepts of mean-index and standard deviation, a ranking method for TIFNs is developed considering the risk preference of Decision Maker (DM). Further, according to the crisp relative closeness coe cient matrix with respect to the normalized TIFNs decision matrix, we use entropy measure to obtain attribute weights. The DMs' weights are calculated by the similarity between the individual and the average decisions. Then, a decision procedure is described to solve the MAGDM under triangular intuitionistic fuzzy environment. Finally, a real trustworthy service selection example is analyzed to verify the practicality and e ectiveness of the developed method.

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“…In this subsection, analogous to the idea of Nan et al [20], the mean value index of a TIFN is de ned as follows.…”

Section: A New Value Index Of Tifns and Ranking Methods 31 The Mean mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

Wan

Xu²

2017

Scientia Iranica

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“…Li et al 8 developed a value and ambiguity based method to rank TIFNs and applied to solve MADM with TIFNs. Nan et al 9 defined the ranking order relations of TIFNs and investigated the fuzzy matrix games with payoffs of TIFNs. The possibility theory of FSs was proposed by Zadeh 10 .…”

Section: Introductionmentioning

confidence: 99%

Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute Group Decision Making with Incomplete Weight Information

Wan¹,

Dong²

2014

IJCIS

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Triangular intuitionistic fuzzy numbers (TIFNs) are a special kind of intuitionistic fuzzy sets (IFSs) on a real number set. TIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The purpose of this paper is on developing a new ranking method of TIFNs and application to multiattribute group decision making (MAGDM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete. The weighted average operator of TIFNs is defined, the concepts of the possibility mean, variance of TIFNs as well as standard deviation are introduced. Hereby two new ranking indices considering the risk attitude of decision maker are developed to rank TIFNs. In the proposed group decision method, the collective overall attribute values of alternatives are obtained by using the weighted average operator of TIFNs We construct the multi-objective programming of maximizing the ranking indices of membership and non-membership functions on alternative's collective overall attribute values, which is transformed into a single linear programming model by using the membership function based weighted sum approach. Thus, the ranking indices of membership and non-membership functions for the alternatives are derived, which are used to rank the alternatives. A personnel selection example is analyzed to demonstrate the applicability, universality and flexibility of the proposed models and method.

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“…Nan et al [54] transformed the intuitionistic fuzzy linear programming problem of such intuitionistic fuzzy matrix games with triangular intuitionistic fuzzy number payoffs into two crisp linear programming problems and used the crisp optimal solutions obtained to get the crisp optimal solution and the intuitionistic fuzzy optimal value of the intuitionistic fuzzy matrix games.…”

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confidence: 99%

A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers

Verma

Kumar

Kacprzyk

2015

JAMRIS

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A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers

Cited by 85 publications

References 26 publications

A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute Group Decision Making with Incomplete Weight Information

A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers

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