Natural n-dimensional fuzzy negations for n-dimensional t-norms and t-conorms

Abstract

N-dimensional fuzzy sets are an extension of fuzzy sets where the membership values are n-tuples of real numbers in the unit interval [0,1] ordered in increasing order, called n-dimensional intervals. The set of n-dimensional intervals is denoted by L n ([0,1]). In the present paper, we consider the definitions and results obtained for n-dimensional fuzzy negations, applying these studies mainly on natural n-dimensional fuzzy negations for n-dimensional triangular norms and triangular conorms. Additionally, the conjugate obtained by action of an n-dimensional automorphism on an n-dimensional natural fuzzy negations for n-dimensional triangular norms and triangular conorms, provides a method to obtain other n-dimensional strong fuzzy negations, in which its properties on L n ([0,1]) are preserved.