Quantitative comparison of similarity measure and entropy for fuzzy sets

Abstract

Comparison and data analysis to the similarity measures and entropy for fuzzy sets are studied. The distance proportional value between the fuzzy set and the corresponding crisp set is represented as fuzzy entropy. We also verified that the sum of the similarity measure and the entropy between fuzzy set and the corresponding crisp set constitutes the total information. Finally, we derive a similarity measure from entropy with the help of total information property, and illustrate a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation. © 2009 Springer.