| Title:
|
Fuzzy distances (English) |
| Author:
|
Bednář, Josef |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
[375]-388 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to $\mathbb{R}^{n}$ are dealt with in detail. (English) |
| Keyword:
|
fuzzy metric |
| Keyword:
|
fuzzy distance |
| Keyword:
|
fuzzy metric space |
| Keyword:
|
fuzzy contraction |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| MSC:
|
11J99 |
| MSC:
|
47H10 |
| MSC:
|
54A40 |
| MSC:
|
54E35 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1249.54013 |
| idMR:
|
MR2181425 |
| . |
| Date available:
|
2009-09-24T20:09:39Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135662 |
| . |
| Reference:
|
[1] Bednář J.: The fuzzy rational database system FSearch 2.0. In: Proc. 6th Internat. Conference on Soft Computing MENDEL, Brno 2000, pp. 232–237 |
| Reference:
|
[2] Bednář J.: Properties of fuzzy metrics on $R^{n}$.In: Proc. East West Fuzzy Colloquium 2002 and 10th Zittau Fuzzy Colloquium, Zittau 2002, pp. 2–6 |
| Reference:
|
[3] Gerla G., Volpe R.: The definition of distance and diameter in fuzzy set theory.Stutia Univ. Babes–Bolyai Math. 31 (1986), 21–26 Zbl 0594.54004, MR 0911862 |
| Reference:
|
[4] Kaleva O., Seikkala S.: On fuzzy metric spaces.Fuzzy Sets and Systems 12 (1984), 215–229 Zbl 0558.54003, MR 0740095, 10.1016/0165-0114(84)90069-1 |
| Reference:
|
[5] Klir G., Yuan B.: Fuzzy Set and Fuzzy Logic: Theory and Applications.Prentice Hall, Englewood Cliffs, NJ 1995 MR 1329731 |
| Reference:
|
[6] Mareš M.: Computation over Fuzzy Quantities.CRC Press, Boca Raton 1994 Zbl 0859.94035, MR 1327525 |
| Reference:
|
[7] Osman A.: Fuzzy metric spaces and fixed fuzzy set theorem.Bull. Malaysian Math. Soc. 6 (1983), 1, 1–4 MR 0733877 |
| Reference:
|
[8] Rudin W.: Real and Complex Analysis.McGraw–Hill, New York 1984 Zbl 1038.00002 |
| Reference:
|
[9] Szmidt E., Kacprzyk J.: Distances between intuitionistic fuzzy sets.Fuzzy Sets and Systems 114 (2000), 505–518 Zbl 0961.03050, MR 1775286, 10.1016/S0165-0114(98)00244-9 |
| . |
