A new pseudo-metric for fuzzy sets

Abstract

A new distance function for fuzzy sets is introduced. It is based on the descriptive complexity, that is, the number of bits (on average) that are needed to describe an element in the symmetric difference of the two sets. The value of the distance gives the amount of additional information needed to describe either one of the two sets when the other is known. We prove that the distance function is a pseudo-metric, namely, it is non-negative, symmetric, it equals zero if the sets are identical and it satisfies the triangle inequality. © 2014 Springer International Publishing.