Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
fuzzy sets; resemblance relation; cuts
fuzzy sets; resemblance relation; cuts
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.
References:
[1] Cock, M. De, Kerre, E.: Why fuzzy T-equivalence relations do not resolve the Poincaré paradox, and related issues. Fuzzy Sets and Systems 133 (2003), 181–192. MR 1949021
[2] Cock, M. De, Kerre, E.: On (un)suitable fuzzy relations to model approximate equality. Fuzzy Sets and Systems 133 (2003), 137–153. MR 1949016 | Zbl 1020.03049
[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.
[4] Kalina, M.: Derivatives of fuzzy functions and fuzzy derivatives. Tatra Mountains Math. Publ. 12 (1997), 27–34. MR 1607135 | Zbl 0951.26015
[5] Šešelja, B., Tepavčević, A.: Completion of ordered structures by cuts of fuzzy sets: an overview. Fuzzy Sets and Systems 136 (2003), 1–19. MR 1978466 | Zbl 1020.06005
[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
[7] Šešelja, B., Tepavčević, A.: Equivalent fuzzy sets. Kybernetika 41 (2005), 115–128. MR 2138763 | Zbl 1249.03088
Search
Partner of
