Analysing Fuzzy Sets Through Combining Measures of Similarity and Distance

TL;DR

This paper proposes a method to combine similarity and distance measures for fuzzy sets, improving the accuracy and interpretability of comparisons in reasoning systems involving large data sets.

Contribution

It introduces a novel combined measure for fuzzy set analysis that reduces ambiguity and enhances automatic comparison capabilities.

Findings

Combined measure reduces ambiguous results

Demonstrations show improved comparison accuracy

Properties of the combined measure are formally analyzed

Abstract

Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs of fuzzy sets. This is particularly a problem where many fuzzy sets are generated from real data, and while two different measures may be used to automatically compare such fuzzy sets, it is difficult to interpret two different results. This is especially true where a large number of fuzzy sets are being compared as part of a reasoning system. This paper introduces a method for combining the results of multiple measures into a single measure for the purpose of analysing and comparing fuzzy sets. The combined measure alleviates ambiguous results and aids in the automatic comparison of fuzzy sets. The properties of the combined measure are given, and demonstrations are presented with discussions on the advantages over using a single measure.