Uncertainties with Atanassov’s intuitionistic fuzzy sets: Fuzziness and lack of knowledge

Pal, Nikhil R.; Bustince, Humberto; Pagola, Miguel; Mukherjee, Utsab; Goswami, Damodar Prasad; Beliakov, Gleb

doi:10.1016/j.ins.2012.11.016

Cited by 89 publications

(41 citation statements)

References 19 publications

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“…As happened with IVFSs, a discrimination should be made between measures yielding scalar or bivalued measurements. This fact is discussed in [17], [110], where the two interpretations of entropy [21], [134] are jointly used to represent the uncertainty linked to an AIFS. We think that it is necessary to carry out a conceptual revision of the definitions of similarity, dissimilarity, entropy, comparability, etc., given for these sets.…”

Section: -Measures Yielding Pairs Each Membership Degree In Amentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

412

159

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Section: -Measures Yielding Pairs Each Membership Degree In Amentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

412

159

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show abstract

“…Szmidt et al (2014) pointed out that entropy alone may not be a satisfactory measure of uncertainty from the point of view of decision making in the IFS context. Pal et al (2013) also acknowledged that entropy and hesitation provide us two different ways of measuring uncertainty for IFSs. They (Pal et al 2013) also suggested that a function, combining these two uncertainties, i.e., entropy (E) and hesitation (π ) could preserve the spirit of addressing total uncertainty of an IFS.…”

Section: Under Intuitionistic Fuzzy Environmentmentioning

confidence: 99%

“…Pal et al (2013) also acknowledged that entropy and hesitation provide us two different ways of measuring uncertainty for IFSs. They (Pal et al 2013) also suggested that a function, combining these two uncertainties, i.e., entropy (E) and hesitation (π ) could preserve the spirit of addressing total uncertainty of an IFS. Now, we would like to comment on this issue in the context of MCDM.…”

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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“…The definitions that are about to be shown, are well known and can be found in several sources, such as [8]. All these definitions, are important to compare both logics, fuzzy and hesitant, and to understand the motivation of the second one.…”

Section: Preliminariesmentioning

confidence: 99%

An axiomatic definition of cardinality for finite interval-valued hesitant fuzzy sets

Quirós¹,

Alonso²,

Dı́az³

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Recently, some extensions of the classical fuzzy sets are studied in depth due to the good properties that they present. Among them, in this paper finite interval-valued hesitant fuzzy sets are the central piece of the study, as they are a generalization of more usual sets, so the results obtained can be immediately adapted to them.In this work, the cardinality of finite intervalvalued hesitant fuzzy sets is studied from an axiomatic point of view, along with several properties that this definition satisfies, being able to relate it to the classical definitions of cardinality given by Wygralak or Ralescu for fuzzy sets.

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Uncertainties with Atanassov’s intuitionistic fuzzy sets: Fuzziness and lack of knowledge

Cited by 89 publications

References 19 publications

A Historical Account of Types of Fuzzy Sets and Their Relationships

A Historical Account of Types of Fuzzy Sets and Their Relationships

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

An axiomatic definition of cardinality for finite interval-valued hesitant fuzzy sets

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