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Zbl 1211.03073
Janiš, Vladimir; Renčová, Magdaléna; Šešelja, Branimir; Tepavčević, Andreja
Cut properties of resemblance. (English)
[J] Kybernetika 46, No. 4, 600-608 (2010). ISSN 0023-5954

Summary: The resemblance relation is used to reflect some real-life situations for which a fuzzy equivalence is not suitable. We study the properties of cuts for such relations. In the case of a resemblance on the real line enriched with a bottom element $-\infty$ under the natural order, $E:=\Bbb R\cup\{-\infty\}$, we show that it determines a special family of crisp functions closely connected to its cut relations. Conversely, we present conditions which should be satisfied by a collection of real functions in $E$ in order that this collection determines a resemblance relation.

MSC 2000:: *03E72 Fuzzy sets (logic)

Keywords: fuzzy sets; resemblance relation; cuts

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