Presented by

Dr. Monoranjan Bhowmik1

Some Results on Generalized Interval-valued Intuitionistic Fuzzy

Sets

IntroductionIn 1965, Zadeh introduced the conceptof fuzzy subsets. Latter many authors generalized the concept of fuzzy subsets in different directions, like veg set, rough set etc.. Atanassov introduced several operations over interval-valued fuzzy set. Pal and Shyamal introduced interval-valued fuzzy matrices and shown several properties of them. After two decades, Atanassov introduced the concept of intuitionistic fuzzy sets (IFSs), which is a generalization of fuzzy subsets.

Several authors present a number of results using IFSs. By the concept of IFSs, first time Pal introduced intuitionistic fuzzy determinant. Latter on Pal and Shyamal introduced intuitionistic fuzzy matrices and distance between intuitionistic fuzzy matrices. Recently Bhowmik and Pal introduced some results on intuitionistic fuzzy matrices and intuitionistic circulant fuzzy matrices and generalized intuitionistic fuzzy matrices.

After the work of Atanassov, again Gargo and Atanassov introduced the interval-valuedintuitionistic fuzzy sets (IVIFSs). They have shown several properties on IVIFSs and shown applications of IVIFSs. Jana andPal studied some operators defined over IVIFS.

Now, we present two fundamental operators defined over fuzzy sets below: On the interval [0,1] (where thefuzzy sets takes their elements) the following operations are defined

Generalized interval-valued intuitionistic fuzzy set (GIVIFS)

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Some relational operations on GIVIFSs

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Some unary and binary operations on GIVIFSs

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Cartesian product of GIVIFSs

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Inverse of R

Two composite operations on GIVIFSs

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Four special types of reflexive of GIVIFRs

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