New Modified Level Operator Nγ Over Intuitionistic Fuzzy Sets

The present paper takes the idea of the level operator N-alpha,N-beta and proposes a modification called N-gamma. The aim of the original level operator is to generate a subset of an intuitionistic fuzzy set A, called (alpha, beta)-set, whose degrees of membership are above a given level (threshold) alpha and degrees of non-membership are below a given level b, where both a, b are fixed numbers in the [0, 1] interval and alpha + beta <= 1. In the modification proposed here, we introduce the operator N-gamma that also generates a subset of an intuitionistic set A, where the elements of the subset are those elements of A, for which the ratio of their degrees of membership to their degrees of non-membership, respectively, is greater or equal to a given number gamma > 0.