An η-Intuitionistic Fuzzy Rings Structure

Abstract

In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research.

Keywords

• averaging operator
• η-intuitionistic fuzzy set
• η-intuitionistic fuzzy ring
• η-intuitionistic fuzzy ideals.