On Atanassov's Intuitionistic Fuzzy Sets in the Complex Plane and the Field of Intuitionistic Fuzzy Numbers

In this paper, we propose a method to construct homeomorphisms from the interior of intuitionistic fuzzy interpretation triangle to the complex plane. Based on such homeomorphisms, we define concepts of pure intuitionistic fuzzy sets and pure intuitionistic fuzzy numbers, and obtain some properties of these new concepts. In addition, we prove that all the pure intuitionistic fuzzy numbers form a field, whose arithmetic operations are given. Finally, we use two numerical examples to show computational skills in such field.

I. Introduction

This paper begins with a solution to a modified version of Open Problem 8 proposed by Atanassov [1]: to find transformations from the complex plane to the interior of intuitionistic fuzzy interpretation triangle (IFIT) and vice versa, in order to acquire more convenient methods for studying different properties of given intuitionistic fuzzy set (IFSs) or of given objects in the complex plane.