A novel similarity measure on intuitionistic fuzzy sets with its applications

Atanassov's intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set that can express and process uncertainty much better. There are various averaging operators defined for IFSs. In this paper, a new type of operator called an intuitionistic fuzzy entropy weighted power average ggregation operator is proposed. The entropy among IFSs is taken into consideration to determine the weights. What's more, the similarity is considered to measure the support degree between two elements of the IFS. Compared with other classical power average operators, the proposed operator is completely driven by data and fully takes into account the relationship among values. Finally, an illustrative example of multiple attribute group decision making is presented to show that the proposed operator is effective and practical. C 2017 Wiley Periodicals, Inc.

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“…Recently, Song et al

\begin{matrix} true \\ right S_{Y} (A, B) & left = \frac{1}{2 n} \sum_{i = 1}^{n} (\sqrt{μ_{A} false(x_{i} false) μ_{B} false(x_{i} false)} + 2 \sqrt{ν_{A} false(x_{i} false) ν_{B} false(x_{i} false)} \\ left + \sqrt{π_{A} false(x_{i} false) π_{B} false(x_{i} false)} + \sqrt{(1 - ν_{A} false(x_{i} false)) (1 - ν_{B} false(x_{i} false))}) \end{matrix}

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Section: Preliminariesunclassified

“…Recently, Song et al 59 proposed a new similarity measure that is based on not only the lower and upper bounds but also the span of the interval, which was defined as…”

Section: Definition 26 a Mapping D: I F S × I F S → [0 1] D(a B)mentioning

confidence: 99%

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Jiang

Wei

Xiang³

et al. 2017

Int. J. Intell. Syst.

111

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“…When a new distance measure is proposed, it is always accompanied with explanations of overcoming counterintuitive cases of other methods and these cases are usually illustrated by single-element IFSs. In [30], Li et al summarized counterintuitive cases proposed by previous literature and constituted an artificial benchmark with six different pairs of single-element IFSs, which has been widely used in the test of distance and similarity measures [31,[44][45][46][47][48][49]. Although these cases cannot represent all counterintuitive situations, they are typical and representative.…”

Section: A Comparison Of Distance Measures For Ifss Based On An Artifmentioning

confidence: 99%

Extended VIKOR Method for Intuitionistic Fuzzy Multiattribute Decision‐Making Based on a New Distance Measure

Luo

Xuanzi

2017

Mathematical Problems in Engineering

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An intuitionistic fuzzy VIKOR (IF-VIKOR) method is proposed based on a new distance measure considering the waver of intuitionistic fuzzy information. The method aggregates all individual decision-makers' assessment information based on intuitionistic fuzzy weighted averaging operator (IFWA), determines the weights of decision-makers and attributes objectively using intuitionistic fuzzy entropy, calculates the group utility and individual regret by the new distance measure, and then reaches a compromise solution. It can be effectively applied to multiattribute decision-making (MADM) problems where the weights of decision-makers and attributes are completely unknown and the attribute values are intuitionistic fuzzy numbers (IFNs). The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by the comparison with the existing method.

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“…Due to the increasing complexity of real life problems, intuitionistic fuzzy set is very suitable for representing fuzzy information under complicated and uncertain settings as an extension of traditional fuzzy set. Intuitionistic fuzzy set theory has been deeply discussed by many scholars since the notations appearance and applied in various fields, such as decision-making [2][3][4][5][6][7], supplier selection [8][9][10], pattern recognition [11][12][13][14], medical diagnosis [15,16], and artificial intelligence [17,18].…”

Section: Introductionmentioning

confidence: 99%

Preference Attitude‐Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection

et al. 2018

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Many applications of intuitionistic fuzzy sets depend on ranking or comparing intuitionistic fuzzy numbers. This paper presents a novel ranking method for intuitionistic fuzzy numbers based on the preference attitudinal accuracy and score functions. The proposed ranking method considers not only the preference attitude of decision maker, but also all the possible values in feasible domain. Some desirable properties of preference attitudinal accuracy and score functions are verified in detail. A total order on the set of intuitionistic fuzzy numbers is established by using the proposed two functions. The proposed ranking method is also applied to select renewable energy. The advantage and validity of the proposed method are shown by comparing with some representative ranking methods.

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A novel similarity measure on intuitionistic fuzzy sets with its applications

Cited by 92 publications

References 34 publications

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Extended VIKOR Method for Intuitionistic Fuzzy Multiattribute Decision‐Making Based on a New Distance Measure

Preference Attitude‐Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection

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