Ranking of interval-valued intuitionistic fuzzy sets

Nayagam, V. Lakshmana Gomathi; Sivaraman, Geetha

doi:10.1016/j.asoc.2011.01.008

Cited by 115 publications

(20 citation statements)

References 38 publications

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“…In the future, the application of the proposed models and methods of SVNSs and INSs needs to be explored in the decision making [86][87][88][89][90][91][92][93][94][95][96][97][98][99], risk analysis and many other uncertain and fuzzy environment [100][101][102][103][104][105][106][107][108][109][110][111][112].…”

Section: Discussionmentioning

confidence: 99%

TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making

Wei

2017

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Abstract:Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued neutrosophic numbers (SVNNs). Firstly, the definition, comparison, and distance of SVNNs are briefly presented, and the steps of the classical TODIM method for MADM problems are introduced. Then, the extended classical TODIM method is proposed to deal with MADM problems with the SVNNs, and its significant characteristic is that it can fully consider the decision makers' bounded rationality which is a real action in decision making. Furthermore, we extend the proposed model to interval neutrosophic sets (INSs). Finally, a numerical example is proposed.

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Section: Discussionmentioning

confidence: 99%

TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making

Wei

2017

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“…Notice that in the above definitions, the hesitancy degree function of IVIFNs is not implemented, which is not the case in the following accuracy degree function introduced by Lakshmana and Sivaraman in [40]:…”

Section: Preliminariesmentioning

confidence: 99%

“…However, as it will be proved later with a counter-example (Example 1), the order relation derived from the application of Xu and Chen's score degree and accuracy degree functions is not total. In a attempt to resolve this drawback, Ye in [39] and Lakshmana Gomathi Nayagam in [40] proposed alternative accuracy degree functions, respectively, which they claimed produced a total ordering of IVIFNs. However, these alternative degree functions are not superior to the existing accuracy degree functions but equivalent 'in the course of comparing any two interval-valued intuitionistic fuzzy numbers'.…”

mentioning

confidence: 99%

A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions

Wu¹,

Chiclana²

2014

Applied Soft Computing

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“…Due to the high complexity of the real world and the limitation of people's judgment, the use of interval-valued intuitionistic fuzzy set has gained much attention [2][3][4][5][6][7][8][9]. As one of the most important applications, the expert system to solve problems under fuzzy environment is a hot research topic [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets Considering Its Hesitancy Degree and Applications in Expert Systems

Luo

et al. 2014

Mathematical Problems in Engineering

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As an important content in fuzzy mathematics, similarity measure is used to measure the similarity degree between two fuzzy sets. Considering the existing similarity measures, most of them do not consider the hesitancy degree and some methods considering the hesitancy degree are based on the intuitionistic fuzzy sets, intuitionistic fuzzy values. It may cause some counterintuitive results in some cases. In order to make up for the drawback, we present a new approach to construct the similarity measure between two interval-valued intuitionistic fuzzy sets using the entropy measure and considering the hesitancy degree. In particular, the proposed measure was demonstrated to yield a similarity measure. Besides, some examples are given to prove the practicality and effectiveness of the new measure. We also apply the similarity measure to expert system to solve the problems on pattern recognition and the multicriteria group decision making. In these examples, we also compare it with existing methods such as other similarity measures and the ideal point method.

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Ranking of interval-valued intuitionistic fuzzy sets

Cited by 115 publications

References 38 publications

TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making

TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making

A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions

A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets Considering Its Hesitancy Degree and Applications in Expert Systems

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