In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...

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...

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...

The aim of this paper is to investigate the fuzzy number intuitionistic fuzzy multiple attribute decision making problems based on the fuzzy number intuitionistic fuzzy sets and Geometric Bonferroni mean operator. Then, we have proposed two aggregation operators: fuzzy number intuitionistic fuzzy geometric Bonferroni mean (FNIFGBM) operator and fuzzy number intuitionistic fuzzy weighted geometr...

For intuitionistic fuzzy sets, it is argued that three dimensional distance functions are not necessary because two dimensional distance functions already provide a simple and concise expression of the distance between two intuitionistic fuzzy sets. However, we show that a three dimensional interpretation of intuitionistic fuzzy sets could give different comparison results to the ones obtained ...

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

As a generalization of fuzzy sets , Atanassov [14] introduced and studied the concept of intuitionistic fuzzy sets park[11] using the idea of intuitionistic fuzzy sets defined the notion of intuionistic fuzzy metric spaces with the help of continuous t-norm and continuous t co-norm as a generalization of fuzzy metric space due to George & veeramani [6] had showed that every metric induces an in...

Most existing distances between intuitionistic fuzzy sets are defined in linear plane representations in 2D or 3D space. Here, we define a new interpretation of intuitionistic fuzzy sets as a restricted spherical surface in 3D space. A new spherical distance for intuitionistic fuzzy sets is introduced. We prove that the spherical distance is different from those existing distances in that it is...

Topology is an important and major area of mathematics and it can give many relationships between other scientific areas and mathematical models.The aim of this paper is to construct intuitionistic fuzzy soft multi topological space and it is shown that an intuitionistic fuzzy soft multi topological space gives a family of parameterized topological spaces and some basic properties regarding wit...