Descriptive-complexity based distance for fuzzy sets

TL;DR

This paper introduces a novel distance measure for fuzzy sets based on descriptive complexity, quantifying the additional information needed to describe one set given another, with proven properties and applications in pattern clustering.

Contribution

It presents a new descriptive-complexity based distance function for fuzzy sets, with theoretical properties and practical clustering applications.

Findings

The distance function is mathematically well-defined and satisfies key properties.

Pattern clustering using this distance yields meaningful groupings.

The method effectively captures informational differences between 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.