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Notes
Convex fuzzy sets
Convex fuzzy sets were originally introduced in Zadeh’s first paper on fuzzy sets “Fuzzy Sets” [Information and Control 12, 1965, 338–353].
Piecewise linear fuzzy sets
We refer to a paper by Pedrycz [FSS 64, 1994, 21–30] for some theoretical and conceptual motivations behind the frequent use of piecewise linear fuzzy sets, in particular of triangular fuzzy sets.
Basically piecewise linear fuzzy sets are used mainly for their simplicity in calculations.
Compact fuzzy sets
There are several variants of the notion of compact fuzzy set to be found, especially in the more mathematically oriented, literature on the subject. One other type, more restrictive than what we introduced, is obtained by asking that the levels/ a (p) would be compact for all a E Io and that also to (µ) would be compact.
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© 1996 Springer Science+Business Media Dordrecht
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Lowen, R. (1996). Special Types of Fuzzy Sets. In: Fuzzy Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8741-9_4
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DOI: https://doi.org/10.1007/978-94-015-8741-9_4
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