On the Choice of Similarity Measures for Type-2 Fuzzy Sets

Similarity measures are among the most common methods of comparing type-2 fuzzy sets and have been used in numerous applications. However, deciding how to measure similarity and choosing which existing measure to use can be difficult. Whilst some measures give results that highly correlate with each other, others give considerably different results. We evaluate all of the current similarity measures on type-2 fuzzy sets to discover which measures have common properties of similarity and, for those that do not, we discuss why the properties are different, demonstrate whether and what effect this has in applications, and discuss how a measure can avoid missing a property that is required. We analyse existing measures in the context of computing with words using a comprehensive collection of data-driven fuzzy sets. Specifically, we highlight and demonstrate how each method performs at clustering words of similar meaning