Triangular Operations, Negations, and Scalar Cardinality of a Fuzzy Set

Scalar approaches to cardinality of a fuzzy set are very simple and convenient, which justifies their frequent use in many areas of applications instead of more advanced and adequate forms such as fuzzy cardinals. On the other hand, theoretical investigations of scalar cardinalities in the hitherto existing subject literature are rather occasional and fragmentary, and lacking in closer references to triangular norms and conorms. This paper is an attempt at filling that gap by constructing an axiomatized theory of scalar cardinality for fuzzy sets with triangular norms and conorms. It brings together all standard scalar approaches, including the so-called sigma-counts and p-powers, and offers infinitely many new alternative options.

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