Descriptive-complexity based distance for fuzzy sets

Abstract

A new distance function dist(A,B) for fuzzy sets A and B is introduced. It is based on the descriptive complexity, i.e., the number of bits (on average) that are needed to describe an element in the symmetric difference of the two sets. The distance gives the amount of additional information needed to describe any one of the two sets given the other. We prove its mathematical properties and perform pattern clustering on data based on this distance.