The Definition of Interval-Valued Intuitionistic Fuzzy Sets in the Framework of Dempster-Shafer Theory

In this report, a critical analysis of conventional operations on interval-valued intuitionistic fuzzy values (\(IVIFVs\)) and their applicability to the solution of multiple criteria decision making (\(MCDM\)) problems in the interval-valued intuitionistic fuzzy setting are presented. It is shown that the classical definition of Atanassov’s interval-valued intuitionistic fuzzy set (\(A\)-\(IVIFS\)) may lead to controversial results. Therefore, a new more constructive definition of \(A\)-\(IVIFS\) is proposed. It is shown that this new definitions makes it possible to present \(IVIFVs\) in the framework of interval-extended Dempster-Shafer theory of evidence (\(DST\)) as belief intervals with bounds presented by belief intervals.

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