Generalized cardinal numbers and operations on them
Fuzzy Sets and SystemsPublished 1 January 1993
Maciej Wygralak
Citations12
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SJR score0.75
SNIP1.25
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TL;DR
A cardinality theory for so-called vaguely defined objects which are mild generalizations of fuzzy sets, obtained by introducing lower and upper approximations of the membership functions, makes use of the sentential calculus in the infinite-valued Łukasiewicz logic.
Abstract
Abstract In this paper we present a cardinality theory for so-called vaguely defined objects which are mild generalizations of fuzzy sets, obtained by introducing lower and upper approximations of the membership functions. The theory makes use of the sentential calculus in the infinite-valued Łukasiewicz logic, and can be applied to fuzzy sets with arbitrary supports, (some kinds of) twofold fuzzy sets, partial sets, etc. The notion of equipotency of vaguely defined objects is studied in detail. The resulting generalized cardinal numbers are convenient tools for describing the powers of vaguely defined objects. In the second part of the paper, basic operations on the generalized cardinals are defined and carefully investigated. Similarities and anomalies in comparison with the classical arithmetic of the usual cardinals are indicated.
Keywords
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