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Scalar and fuzzy cardinalities of crisp and fuzzy multisets
Author(s) -
Casasnovas Jaume,
Rosselló Francesc
Publication year - 2009
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20350
Subject(s) - mathematics , axiom , fuzzy logic , scalar (mathematics) , fuzzy set , finite set , discrete mathematics , axiomatic system , fuzzy number , set (abstract data type) , algebra over a field , computer science , pure mathematics , artificial intelligence , mathematical analysis , geometry , programming language
We define in an axiomatic way scalar and fuzzy cardinalities of finite multisets over ]0, 1], and we obtain explicit descriptions for them. We show that, for multisets over ]0, 1] associated to finite fuzzy sets, the cardinalities defined in this study are equivalent to the cardinalities of the corresponding fuzzy sets previously introduced in the literature. Finally, we also define in an axiomatic way scalar and fuzzy cardinalities of finite fuzzy multisets over any set X , and we use the descriptions of the cardinalities of finite multisets over ]0, 1] to obtain explicit characterizations of the former. © 2009 Wiley Periodicals, Inc.