The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. The purpose of this paper is to introduce a generalization of ideas presented in [20]. Indeed, we study the concept of intuitionistic fuzzy interior ideals of a Γ-semigroup, by using Atanassov’s idea and investigate some of their important properties. Specially, we obtain a chara...

Recently, F.Smarandache generalized the Atanassov’s intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets. Also, this author de…ned the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in this work that this is false.

A new concept of the inclusion measure for intuitionistic fuzzy sets is proposed by the axiomatic definition. Also, the distance measures, similarity measures and information entropy are recalled and summarized. Most of important, some relationships among distance measure, information entropy, and inclusion measure of IFSs are then investigated. Finally, we obtain some important theorems by whi...

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. Using the notion of intuitionistic fuzzy sets, Çoker [5] introduced the notion of intuitionistic fuzzy topological spaces. In this paper, we define the notion of intuitionistic fuzzy semiopen (r...

Study about fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Unlike fuzzy set, IFSs contains uncertainty named hesistancy, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of ununified entropy definition. By considering different fuzzy entropy definitions, fuzzy entropy is designed and...

Study of fuzzy entropy on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Built in uncertainty in IFSs, it is named as hesitance. It is contained in fuzzy membership function in itself by definition. Hence, designing fuzzy entropy is not easy because there is no general entropy definition about IFSs. By considering existing fuzzy entropy definitions, fuzzy entropy on IFSs is desig...

In recent years, there have been a growing interest in developing Multi-Criteria Decision Making (MCDM) and Group Decision Making (GDM) using type-2 fuzzy sets and Intuitionistic Fuzzy Sets (IFSs) which provide frameworks to handle the encountered uncertainties in decision making models. Previous research has shown the power of type-2 fuzzy logic systems to handle the linguistic uncertainties. ...

In this paper, we revisit the notion of inclusion for intuitionistic fuzzy sets (IFSs). Applying the extended modal logic operators Dα over IFSs, we construct a new class of two–valued inclusion indicators; we compare it to the original proposal from [1]; and finally we exploit it to define an intuitively meaningful notion of graded inclusion indicators over IFSs, parallelling and clarifying ea...

In this paper, we propose new method to calculate the distance between intuitionistic fuzzy sets (IFSs) based on three dimensional representation of IFSs and analyze relations similarity measure IFSs. Finally, apply proposed measures pattern recognitions.

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...