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In this paper, different types of interval cut-set of interval-valued intuitionistic fuzzy sets (IVIFSs), complement of these cut-sets are defined. Some properties of those cut-set of IVIFSs are investigated. Also three decomposition theorems of IVIFSs are defined. These works can also be used in setting up the basic theory of IVIFSs.

If in an intuitionistic fuzzy matrix each element is again a smaller intuitionistic fuzzy matrix then the intuitionistic fuzzy matrix is called intuitionistic fuzzy block matrix (IBFMs). In this paper, the concept of intuitionistic fuzzy block matrices (IBFMs) are introduced and defined different types of intuitionistic fuzzy block matrices (IBFMs). The… (More)

In this chapter, the authors establish decomposition theorems of Generalized Interval-Valued Intuitionistic Fuzzy Sets (GIVIFS) by use of cut sets of generalized interval-valued intuitionistic fuzzy sets. First, new definitions of eight kinds of cut sets generalized interval-valued intuitionistic fuzzy sets are introduced. Second, based on these new cut… (More)

In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0,1]. Some properties of GIVIFMs are studied using the… (More)

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