Generalised Atanassov Intuitionistic Fuzzy Sets

Abstract

When Atanssov created Intuitionistic Fuzzy Sets, he imposed the condition that the sum of membership and non-membership values for each point in the universe of discourse should be less than or equal to one. We challenge this constraint and define some new types of Intuitionistic Fuzzy Sets such that, for any point in the universe of discourse, the sum of membership and non-membership values can be greater than one, or their difference can be negative or positive, while one value is greater than the other, or the sum of their squares is less than or equal to one.