Abstract
We revisit the relational study between different axiomatic definitions of similarity and dissimilarity of fuzzy sets developed in two previous articles. We observe that every axiomatic definition admits two variants, depending on whether we assume that the measure fulfills the corresponding properties when we restrict ourselves to a fixed finite cardinal universe, or that it complies with them in a general universe. The results and counterexamples presented in those articles concern the implication relations between different axiomatic notions, and they implicitly consider a general finite universe (whose cardinality is not fixed in advance). Most of them fit both variants, but some others need to be adapted, in order to meet the first option. In this short note, we offer the adapted versions of the corresponding results and counterexamples.
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