Abstract
This chapter presents some elements of fuzzy set theory. Similarly to a set, a fuzzy set is a collection of elements in a universe of discourse. However, their membership in that collection is graduated. This feature implies that the logical basis of fuzzy sets must be many-valued logic, i.e. logic allowing intermediate logical values lying between 0 (false) and 1 (true). The concept of a fuzzy set and fundamentals of many-valued sentential calculus will be presented in the first section. In the next three sections, we deal with triangular norm-based operations on fuzzy sets as well as other basic elements of the language of fuzzy sets. The last section of this chapter contains an introduction to the problem of cardinalities of fuzzy sets with triangular norm-based operations.
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© 2003 Springer-Verlag Berlin Heidelberg
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Wygralak, M. (2003). Fuzzy Sets. In: Cardinalities of Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36382-8_2
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DOI: https://doi.org/10.1007/978-3-540-36382-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53514-7
Online ISBN: 978-3-540-36382-8
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