Rough set theory introduced by Pawlak [8] is based on equivalence relations. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. The basic rough set model was extended to rough set model...

The (α, β) cut of an Intuitionistic Fuzzy Set (IFS) was studied by P. K. Sharma [4]. In this paper we introduce a new type of cut strong (α, β) cut of IFS and study their properties. Also three decomposition theorems are discussed.

Introduction The central idea of Synthetic Domain Theory (SDT) is that, if one formalizes abstract properties that a category of domains should have (relative to an intended range of applications), one might nd full subcategories of the category of sets enjoying these properties. Domains, then, would just be (special) sets, maps of domains would be arbitrary set-theoretic functions, and various...

Uninorms are a generalization of t-norms and tconorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In reallife applications, this kind of aggregation may be counter-intuitive. Atanassov’s i...

On 2005, F. Smarandache generalized the Atanassov’s intuitionistic fuzzy setsto neutrosophic sets. Also, this author and some co-workers introduced the notion of interval neutrosophic set, which is an instance of neutrosophic set and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. We study in this paper relations between i...

In this paper, we present the concept of relations in intuitionistic fuzzy soft set and study some of their properties and also discuss symmetric, transitive and reflexive intuitionistic fuzzy soft relations.

In this paper we have introduced the concept of intuitionistic fuzzy soft matrix and defined different types of matrices along with some new operations in the parlance of intuitionistic fuzzy soft set theory. Then based on some of these new matrix operations a new efficient methodology named as IFSM -Algorithm has been developed to solve intuitionistic fuzzy soft set based group decision making...

The thesis consists of three sections, developing models of intuitionistic set theory in suitable categories. First, the categorical framework in which models are constructed is reviewed, and the theory of all such models, called Basic Intuitionistic Set Theory (BIST), is stated; second, we give a notion of an ideal over a category, with which one can build a model of BIST in which a given topo...