An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets

Zhang, Xu; Chen, J.

doi:10.1142/s0218488508005406

Cited by 333 publications

(161 citation statements)

References 29 publications

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“…The normalized Minkowski distance is a distance measure [29][30][31][32][33][34] that generalizes a wide range of distances such as the normalized Hamming distance and the normalized Euclidean distance. In fuzzy set theory, it can be useful, for example, for the calculation of distances between fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, etc.…”

Section: Normalized Minkowski Distancementioning

confidence: 99%

A New Minkowski Distance Based on Induced Aggregation Operators

Merigó¹,

Ramón²

2011

IJCIS

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The Minkowski distance is a distance measure that generalizes a wide range of distances such as the Hamming and the Euclidean distance. In this paper, we develop a generalization of the Minkowski distance by using the induced ordered weighted averaging (IOWA) operator. We call it the induced Minkowski OWA distance (IMOWAD) or induced generalized OWA distance (IGOWAD) operator. Then, we are able to obtain a wide range of distance measures that includes the Minkowski distance, the Minkowski OWA distance (MOWAD), and the induced OWA distance (IOWAD). We also present a further generalization by using quasi-arithmetic means. We end the paper with a numerical example of the new approach.

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Section: Normalized Minkowski Distancementioning

confidence: 99%

A New Minkowski Distance Based on Induced Aggregation Operators

Merigó¹,

Ramón²

2011

IJCIS

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“…Although various types of distance measures between IFSs were proposed over the past several years and most of them satisfies the distance axioms (Definition 5), some unreasonable cases can still be found [31,32]. For example, consider three single-element IFSs = ( , 0.4, 0.2), = ( , 0.5, 0.3), and = ( , 0.5, 0.2).…”

Section: Analysis On Existing Distance Measures Between Ifssmentioning

confidence: 99%

“…To some extent, the amount of computation is increased, and the results are not concise as the crisp value obtained by distance measure. Also, some researchers [30][31][32] reviewed existing distance and similarity measures between IFSs and tested them with an artificial benchmark. The result showed that many existing distance measures generate counterintuitive cases and fail to capture waver, the lack of knowledge, which should have been an advantage of IFSs.…”

Section: Introductionmentioning

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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“…Since the introduction of intuitionistic fuzzy sets proposed by Atanassov [28], the intuitionistic fuzzy decision-making has become a promising topic [29,30]. Intuitionistic linguistic variables [31] are discussed in the decision-making process, and the distance and similarity measures of intuitionistic fuzzy sets [32] are presented. In order to extend uncertain theory and develop its applications, Pei [33] introduced intuitionistic fuzzy variables and developed outranking methods for evaluating intuitionistic fuzzy variables.…”

Section: Introductionmentioning

confidence: 99%

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

Jin

2018

Mathematical Problems in Engineering

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Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.

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An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets

Cited by 333 publications

References 29 publications

A New Minkowski Distance Based on Induced Aggregation Operators

A New Minkowski Distance Based on Induced Aggregation Operators

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

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

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