As an extension of the intuitionistic fuzzy set, intuitionistic trapezoidal fuzzy set is an invaluable mathematical theory to express uncertain phenomenon in our real word. In this article, the aggregation methods of the intuitionistic trapezoidal fuzzy information are chief researched. Firstly, the generalized aggregation operator is introduced for aggregating intuitionistic trapezoidal fuzzy ...

We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some ...

In this paper we introduce the concentration and dilation operators on interval valued intuitionistic fuzzy soft sets of root type which is a generalization of fuzzy set, intuitionistic fuzzy set, interval valued intuitionistic fuzzy set and intuitionistic fuzzy set of root type and establish some properties of these operators. We define Hamming distance between two interval valued intuitionist...

Paraconsistent intuitionistic fuzzy set is an extension of intuitionistic fuzzy set or interval-valued fuzzy set. It relaxes the requirement that t + f ≤ 1, where t is grade of truth-membership and f is grade of false-membership. In paraconsistent intuitionistic fuzzy set, t, f ∈ [0, 1], 0 ≤ t + f ≤ 2. In this paper, we present a generalization of the relational model of data based on paraconsi...

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...

We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees...

In this paper, Symmetric Trapezoidal Intuitionistic Fuzzy Numbers (STIFNs) have been introduced and their desirable properties are also studied. A new type of intuitionistic fuzzy arithmetic operations for STIFN have been proposed based on ( , )   -cuts. A numerical example is considered to elaborate the proposed arithmetic operations. These operations find applications in solving linear prog...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

Intuitionistic fuzzy special sets is a special case of intuitionistic fuzzy sets. In this paper, under the framework of information systems, the relationship between intuitionistic fuzzy special sets and rough sets is analyzed. Based on basic intuitionistic fuzzy special sets of information systems, intuitionistic fuzzy special σ-algebra are generated, and rough sets are embedded in the intuiti...