In this paper the concept of interval valued intuitionistic fuzzy soft set relations (IVIFSS-relations for short) is proposed. Our relations on interval valued intuitionistic fuzzy soft sets is an extension of the relations on intuitionistic fuzzy soft sets, introduced by Mukherjee and Chakraborty in 2009. The basic properties of the IVIFSS-relations are also presented and discussed. It is seen...

In this paper, we define some results on generalized interval-valued intuitionistic fuzzy sets (GIVIFSs). In fact, all interval-valued intuitionistic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. We define two composite relations, four types of reflexivity and irreflexivity of GIVIFSs with some of their properties. We define generalized interval-valued intuitionistic fuzzy rel...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

In this paper, we introduce  the notions of   interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals    of   BCI algebras   and investigate some of their properties.   We then derive characterization theorems for these generalized interval-valued fuzzy ideals  and discuss their relationship.

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...