| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2010-10-22T05:20:01Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140773 |
| . |
| Reference:
|
[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 |
| Reference:
|
[2] Cock, M. De, Kerre, E.: On (un)suitable fuzzy relations to model approximate equality.Fuzzy Sets and Systems 133 (2003), 137–153. Zbl 1020.03049, MR 1949016 |
| 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. |
| Reference:
|
[4] Kalina, M.: Derivatives of fuzzy functions and fuzzy derivatives.Tatra Mountains Math. Publ. 12 (1997), 27–34. Zbl 0951.26015, MR 1607135 |
| 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 |
| . |
