On a reflexivity-preserving family of cardinality-based fuzzy comparison measures

In this paper, we generalize and extend previous work on a triparametric family of cardinality-based fuzzy similarity measures. More specifically, we (i) generalize this family to a broader family of fuzzy comparison measures, (ii) summarize previously obtained results regarding this family and fill up a few gaps by adding some novel results, (iii) compare our parametric family with an already existing one, and (iv) elaborate on the ranking invariance between certain members of the presented triparametric family of cardinality-based fuzzy comparison measures.