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...

Generally fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory has been used for analyzing the fuzzy system reliability. To analyze the fuzzy system reliability, the reliability of each component of the system is considered as a triangular intuitionistic fuzzy number. At first triangular intuitionistic fuzzy number and their arithmetic operations are...

In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov’s intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these se...

Molodtsov first proposed the soft set theory, which can be used as a general mathematical tool for dealing with fuzzy and uncertain information. As a generalization of soft set, interval-valued intuitionistic fuzzy soft set is another soft set structure,it is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The objective of this paper is to study the decision making ...

Intuitionistic fuzzy sets theory which is the generalisation of fuzzy sets theory is more suitable tool for dealing with imprecise information. The information provided by the decision maker is imprecise in many situations. So, intuitionistic fuzzy preference relation is a suitable tool for such cases. The estimation of the priority vector of the intuitionistic fuzzy preference relation is an i...

The concepts of fuzzy θ-open (θ-closed)sets and fuzzy θ-closure operator are introduced and discussed in intuitionistic fuzzy topological spaces. As applications of these concepts, certain functions are characterized in terms of intuitionistic fuzzy θ-closure operator.

In general fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory for analyzing the fuzzy system reliability has been used. To analyze the fuzzy system reliability, the reliability of each component of the system as a triangular intuitionistic fuzzy number is considered. Triangular intuitionistic fuzzy number and their arithmetic operations are introdu...

Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further...