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Title: Cut properties of resemblance (English)
Author: Janiš, Vladimir
Author: Renčová, Magdaléna
Author: Šešelja, Branimir
Author: Tepavčević, Andreja
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 46
Issue: 4
Year: 2010
Pages: 600-608
Summary lang: English
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Category: math
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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 a real line $E$ 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. (English)
Keyword: fuzzy sets
Keyword: resemblance relation
Keyword: cuts
MSC: 04A72
idZBL: Zbl 1211.03073
idMR: MR2722090
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Date available: 2010-10-22T05:20:01Z
Last updated: 2013-09-21
Stable URL: http://hdl.handle.net/10338.dmlcz/140773
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Reference: [3] Janiš, V., Renčová, M., Šešelja, B., Tepavčević, A.: Construction of fuzzy relation by closure systems.In: PReMI 2009 (S. Chaudhury et al., eds.), LNCS 5909, Springer-Verlag, Berlin – Heidelberg 2009, pp. 116–121.
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Reference: [5] Šešelja, B., Tepavčević, A.: Completion of ordered structures by cuts of fuzzy sets: an overview.Fuzzy Sets and Systems 136 (2003), 1–19. Zbl 1020.06005, MR 1978466
Reference: [6] Šešelja, B., Tepavčević, A.: Representing ordered structures by cuts of fuzzy sets: an overview.Fuzzy Sets and Systems 136 (2003), 21–39. MR 1978467
Reference: [7] Šešelja, B., Tepavčević, A.: Equivalent fuzzy sets.Kybernetika 41 (2005), 115–128. Zbl 1249.03088, MR 2138763
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