On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge

Guo, Ke; Qi, Song

doi:10.1016/j.asoc.2014.07.006

Cited by 77 publications

(50 citation statements)

References 28 publications

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“…A number of studies focused on information measures (distance measure, similarity measure, entropy, inclusion measure) for IFSs and discussed their transformation relationships. However, few studies paid close attention to the information measures for Pythagorean fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

Pythagorean Fuzzy Information Measures and Their Applications

Peng

Yuan

Yang

2017

Int. J. Intell. Syst.

315

198

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Pythagorean fuzzy set (PFS), originally proposed by Yager, is more capable than intuitionistic fuzzy set (IFS) to handle vagueness in the real world. The main purpose of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for PFSs. The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs. For achieving this goal, some new formulae for information measures of PFSs are introduced. To show the efficiency of the proposed similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings and also demonstrate their practicality and effectiveness of similarity measure between PFSs.

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Section: Introductionmentioning

confidence: 99%

Pythagorean Fuzzy Information Measures and Their Applications

Peng

Yuan

Yang

2017

Int. J. Intell. Syst.

315

198

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“…Although these aforementioned works have greatly enriched the theory of PFSs, to our best knowledge, there is few study about the entropy in the setting of PFSs. Entropy is a vital measure of fuzzy or uncertain information in the IFS theory, which has received great attention . Burille and Bustince proposed the definition and the formula of intuitionistic fuzzy entropy (IFE) based on how far the IFS is from being a FS to describe the fuzziness degree of IFS.…”

Section: Introductionmentioning

confidence: 99%

Pythagorean Fuzzy LINMAP Method Based on the Entropy Theory for Railway Project Investment Decision Making

Xue

Zhang

et al. 2017

Int. J. Intell. Syst.

136

109

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The uncertainty and complexity of the decision-making environment and the subjectivity of the decision makers will lead to the inevitable errors of the decision-making data. A poor decision will be produced with those errors, whereas the linear programming technique for multidimensional analysis of preference (LINMAP) method can adjust such errors through constructing an optimal programming model based on the consistency of the decision-making information, and it has been applied widely in multiple attribute group decision making (MAGDM). Moreover, Pythagorean fuzzy information is useful to simulate the ambiguous and uncertain decision-making environment. Therefore, the LINMAP method under the Pythagorean fuzzy circumstance will be proposed in this paper to solve MAGDM problems. To measure the fuzziness and uncertainty of Pythagorean fuzzy set (PFS) and interval-valued PFS, Pythagorean fuzzy entropy (PFE) and interval-valued PFE (IVPFE) grounded on the similarity and hesitancy parts have been defined, respectively. Then, Pythagorean fuzzy LINMAP (PF LINMAP) methods are constructed on the basis of the PFE and IVPFE correspondingly. Under the given preference relations, the maximum consistency and the amount of knowledge can be realized by the proposed methods. After investigating the relevant indicator system, the decision-making problem concerning railway project investment has been solved through the proposed PF LINMAP method with PFE. Finally, the practicability and effectiveness of the PF LINMAP method has been verified via the comparative analysis with the existing methods. C 2017 Wiley Periodicals, Inc.

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“…Based on the distance between an IFS and its complement with the combination of hesitation, Guo and Song (2014) introduced a new entropy which is defined as follows:…”

Section: Under Intuitionistic Fuzzy Environmentmentioning

confidence: 99%

Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set

Das

Guha

2015

Soft Comput

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The aim of this study is to propose an objective method for determining weights of criteria (also called attributes) based on a new measure of intuitionistic fuzzy information, called knowledge measure, in a real-world multi-criteria decision-making problem under intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. To address this issue, we first analyze the existing entropy measures and show that their use in objective weight determination process may lead us to produce unreliable weights of criteria by citing appropriate examples. Then we analyze important properties of knowledge measure of intuitionistic fuzzy set (IFS) and also define knowledge measure for interval-valued intuitionistic fuzzy set. Then a new method to determine the weights of criteria is developed on the basis of knowledge measure where information about criteria weights is completely unknown and partly known. A real-life example is presented to illustrate the proposed weight determination method and a comparative analysis is carried out to indicate the practicality and effectiveness of knowledgebased weight-generation method under both intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. Finally, we formulate the axioms for knowledge measure associated with IFSs and we also propose families (classes) of knowledge measures.

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On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge

Cited by 77 publications

References 28 publications

Pythagorean Fuzzy Information Measures and Their Applications

Pythagorean Fuzzy Information Measures and Their Applications

Pythagorean Fuzzy LINMAP Method Based on the Entropy Theory for Railway Project Investment Decision Making

Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set

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