A study of similarity measures through the paradigm of measurement theory: the fuzzy case

摘要

We extend to fuzzy similarity measures the study made for classical ones in a companion paper (Coletti and Bouchon-Meunier in Soft Comput 23:6827-6845, 2019). Using a classic method of measurement theory introduced by Tversky, we establish necessary and sufficient conditions for the existence of a particular class of fuzzy similarity measures, representing a binary relation among pairs of objects which expresses the idea of "no more similar than". In this fuzzy context, the axioms are strictly dependent on the combination operators chosen to compute the union and the intersection.