The concept of an intuitionistic fuzzy set can be reconsidered as an approach for defining a fuzzy set In cases where the available information is not enough to define an inaccurate concept of an ordinary fuzzy set. In sum, the theory of fuzzy sets is generalized intuitionistic fuzzy sets. It seems that quantitative research on multiattribute or multi-criteria decision making problems have been...

Soft set theory, fuzzy set theory and rough set theory are all mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the discussions of the combinations of intervalvalued intuitionistic fuzzy set,...

In 1966, (Imai and Iseki, 1966) defined a class of algebras of type (2, 0) named BCK-algebras. At the same time, (Iseki, 1966) generalized another class of algebras of type (2, 0) called BCI-algebras. Hu and Li (1983) introduced the concept of BCH-algebras and gave examples of proper BCH-algebras (Hu and Li, 1985). Neggers and Kim (2001) introduced and investigated a class of algebras, viz., th...

Abstract Assuming that ∗ is any operation defined on a product set X × Y and taking values on a set Z,it can be extended to intuitionistic fuzzy sets by means of the extended form of the Zadeh’s extension principle for the intuitionistic fuzzy sets. Given an IFS C of Z, it is here shown how to solve the equation A ∗ B = C (or A ∗ B ⊆ C) when an intuitionistic fuzzy subset A of X (or an intuitio...

Let G = (V,E) be the IFG and D be set of vertices, then D is said to be Intuitionistic point set dominating set of G if for every S⊆ VD there exists a node d ∈ D such that the Intuitionistic fuzzy sub graph < S∪{d} > induced by S∪{d} is a connected Intuitionistic fuzzy graph. In this paper we study some results on Intuitionistic Point set dominating set and its number of IFGs. Also we establish...

In this paper basic notions of rough intuitionistic fuzzy set in semigroups are given and we discuss some of its basic properties. We introduce the notions of rough intuitionistic fuzzy left (right, two-sided, bi-, (1, 2)-) ideals in a semigroup and give some properties of such ideals.

In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are pointed out.

The dominance–based rough set approach plays an important role in the development of the rough set theory. It can be used to express the inconsistencies coming from consideration of the preference–ordered domains of the attributes. The purpose of this paper is to further generalize the dominance–based rough set model to fuzzy environment. The constructive approach is used to define the intuitio...

A new concept to the optimization problem in an intuitionistic fuzzy environment is introduced. A general model, of linear programming problems in which both the right hand side constants and the technological coefficients are intuitionistic fuzzy numbers, has been presented. An attempt has been made to find a general linear non-membership function and intuitionistic fuzzy index together with t...

Abstract. With respect to multi-attribute decision making under uncertain linguistic environment, a new interval-valued 2-tuple linguistic representation model is introduced. To deal with the situation where the elements in a set are interdependent, several generalized interval-valued 2-tuple linguistic correlated aggregation operators are defined. It is worth pointing out that some intervalval...