Variants of Defining the Cardinalities of Fuzzy Sets
Cardinality, one of the most basic characteristics of a fuzzy set, is a notion having many applications. One of them is elementary probability theory of imprecise events. Fuzzy and nonfuzzy approaches to probabilities of events like “a ball drawn at random from an urn containing balls of various sizes is large” do require an appropriate notion of the cardinality of a fuzzy set, e.g. of the fuzzy set of large balls in an urn. Contemporary fuzzy set cardinality theory offers a variety of options, including the use of triangular norms. This paper presents their overview encompassing scalar approaches as well as approaches in which cardinalities of fuzzy sets are themselves fuzzy sets of usual cardinals.
KeywordsValuation Property Triangular Norm Fuzzy Probability Cauchy Functional Equation Scalar Cardinality
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