A BIPARAMETRIC FAMILY OF CARDINALITY-BASED FUZZY SIMILARITY MEASURES

We present a systematic way of constructing and analyzing fuzzy similarity measures based on cardinality. This is achieved by introducing a general form for such measures, that depends on two parameters. We demonstrate that this general form includes several existing families of fuzzy similarity measures. Moreover, we show that certain properties can be ensured by imposing simple constraints on the parameters. In particular, we present constraints that ensure several forms of restrictability, which allow to reduce the calculation time in practical implementations. To conclude, we illustrate the presented technique by using it to analyze some well-known fuzzy similarity measures.