The operations on intuitionistic fuzzy values in the framework of Dempster–Shafer theory

Dymova, Ludmila; Sevastjanov, Pavel

doi:10.1016/j.knosys.2012.04.026

Cited by 74 publications

(59 citation statements)

References 45 publications

(122 reference statements)

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“…In [27] it was confirmed that correct results cannot always be obtained by the method of comparing the intuitionistic fuzzy numbers introduced in [28].…”

Section: Introductionmentioning

confidence: 92%

“…Two approaches of formulating the operation on belief intervals are suggested in paper [27]. The first approach is based on a probability interpretation of belief intervals.…”

Section: Operations On Ifvs In Framework Of Dstmentioning

confidence: 99%

“…A few limitations of traditional operations on fuzzy values were conferred in [26]. In [27], appropriate critical examples can be read about.…”

Section: Introductionmentioning

confidence: 99%

“…In paper [27], it was demonstrated that the use of the Dempster-Shafer theory based on converting intuitionistic fuzzy values to belief intervals allows one to achieve results which are more reliable, as well as facilitates the calculations in the solution of the MCDM problem. However, when using the conversion of the intuitionistic fuzzy values is not appropriate, using the heuristic method of raising intuitionistic fuzzy values to intuitionistic fuzzy power is advisable.…”

Section: Introductionmentioning

confidence: 99%

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An approach to exponentiation with interval-valued power

Tikhonenko-Kędziak¹,

Kurkowski²

2016

J. Appl. Math. Comput. Mech.

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Abstract. The main aim of the work is introducing an operation of raising intuitionistic fuzzy values to intuitionistic fuzzy power, which not requiring to conversion of intuitionistic fuzzy values. Introducing an operation of raising intuitionistic fuzzy values to intuitionistic fuzzy power, which does not require conversion of intuitionistic fuzzy values is the main aim of the work. It is known that, in the classical intuitionistic fuzzy sets theory, the use of all aggregation modes is not always possible because of the lack of definition of raising intuitionistic fuzzy values to intuitionistic fuzzy power. Therefore, the specific aim of the work is to present the heuristic method of raising intuitionistic fuzzy values to intuitionistic fuzzy power, and the consideration of its properties.

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“…In [27] it was confirmed that correct results cannot always be obtained by the method of comparing the intuitionistic fuzzy numbers introduced in [28].…”

Section: Introductionmentioning

confidence: 92%

“…Two approaches of formulating the operation on belief intervals are suggested in paper [27]. The first approach is based on a probability interpretation of belief intervals.…”

Section: Operations On Ifvs In Framework Of Dstmentioning

confidence: 99%

“…A few limitations of traditional operations on fuzzy values were conferred in [26]. In [27], appropriate critical examples can be read about.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An approach to exponentiation with interval-valued power

Tikhonenko-Kędziak¹,

Kurkowski²

2016

J. Appl. Math. Comput. Mech.

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“…Rashmanlou et al [22] formulated the concept of IVIF graphs and gave a detailed description on IVIF graphs and their properties. Dymova and Sevastjanov [23] extended Dempster-Shafer theory over IVIF for solving GDM problems effectively. Another interesting area of concern for researchers in IVIF lies in consistency checks and preference completion [24,25].…”

Section: Introductionmentioning

confidence: 99%

A Scientific Decision Framework for Supplier Selection under Interval Valued Intuitionistic Fuzzy Environment

Krishankumar

Ravichandran

Ramprakash

2017

Mathematical Problems in Engineering

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This paper proposes a new scientific decision framework (SDF) under interval valued intuitionistic fuzzy (IVIF) environment for supplier selection (SS). The framework consists of two phases, where, in the first phase, criteria weights are estimated in a sensible manner using newly proposed IVIF based statistical variance (SV) method and, in the second phase, the suitable supplier is selected using ELECTRE (ELimination and Choice Expressing REality) ranking method under IVIF environment. This method involves three categories of outranking, namely, strong, moderate, and weak. Previous studies on ELECTRE ranking reveal that scholars have only used two categories of outranking, namely, strong and weak, in the formulation of IVIF based ELECTRE, which eventually aggravates fuzziness and vagueness in decision making process due to the potential loss of information. Motivated by this challenge, third outranking category, called moderate, is proposed, which considerably reduces the loss of information by improving checks to the concordance and discordance matrices. Thus, in this paper, IVIF-ELECTRE (IVIFE) method is presented and popular TOPSIS method is integrated with IVIFE for obtaining a linear ranking. Finally, the practicality of the proposed framework is demonstrated using SS example and the strength of proposed SDF is realized by comparing the framework with other similar methods.

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Belief and Plausibility Functions on Intuitionistic Fuzzy Sets

Hwang

Yang

2015

Int. J. Intell. Syst.

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Belief and plausibility functions based on Dempster-Shafer theory have been used to measure uncertainty. They are also widely studied and applied in diverse areas. Numerous studies in the literature have presented various generalizations of belief and plausibility functions to fuzzy sets. However, there are still less generalizations of belief and plausibility functions to intuitionistic fuzzy sets. Because intuitionistic fuzzy sets can present the degrees of both membership and nonmembership with a degree of hesitancy, the knowledge and semantic representation becomes more general and applicable than fuzzy sets. In this paper, we propose a generalization of belief and plausibility functions to intuitionistic fuzzy sets based on fuzzy integral. Some numerical examples show the effectiveness of the proposed generalization. Furthermore, this generalization of belief and plausibility functions to intuitionistic fuzzy sets is able to catch more information about the change of intuitionistic fuzzy focal elements. C 2015 Wiley Periodicals, Inc.

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The operations on intuitionistic fuzzy values in the framework of Dempster–Shafer theory

Cited by 74 publications

References 45 publications

An approach to exponentiation with interval-valued power

An approach to exponentiation with interval-valued power

A Scientific Decision Framework for Supplier Selection under Interval Valued Intuitionistic Fuzzy Environment

Belief and Plausibility Functions on Intuitionistic Fuzzy Sets

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