| Title:
|
Characterization of fuzzy order relation by fuzzy cone (English) |
| Author:
|
Kon, Masamichi |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
58 |
| Issue:
|
5 |
| Year:
|
2022 |
| Pages:
|
779-789 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed convex cones. (English) |
| Keyword:
|
fuzzy order relation |
| Keyword:
|
fuzzy cone |
| MSC:
|
03E72 |
| MSC:
|
18B35 |
| idZBL:
|
Zbl 07655859 |
| idMR:
|
MR4538625 |
| DOI:
|
10.14736/kyb-2022-5-0779 |
| . |
| Date available:
|
2023-01-23T16:33:43Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151303 |
| . |
| Reference:
|
[1] Jahn, J., Ha, T. X. D.: New order relations in set optimization..J. Optim. Theory Appl. 148 (2011), 209-236. |
| Reference:
|
[2] Khan, A. A., Tammer, C., Z\u{a}linescu, C.: Set-valued Optimization: An Introduction with Applications..Springer-Verlag, Berlin 2015. |
| Reference:
|
[3] Kon, M.: Fuzzy Set Optimization (in Japanese)..Hirosaki University Press, Japan 2019. |
| Reference:
|
[4] Kon, M., Kuwano, H.: On sequences of fuzzy sets and fuzzy set-valued mappings..Fixed Point Theory Appl. 2013 (2013), 327. |
| Reference:
|
[5] Kuroiwa, D., Tanaka, T., Ha, T. X. D.: On cone convexity of set-valued maps..Nonlinear Analysis, Theory, Methods Appl. 30 (1997), 1487-1496. |
| Reference:
|
[6] Peressini, A. L.: Ordered Topological Vector Spaces..Harper and Row, New York 1967. |
| Reference:
|
[7] Young, R. C.: The algebra of many-valued quantities..Math. Ann. 104 (1931), 260-290. |
| Reference:
|
[8] Zadeh, L. A.: Fuzzy sets..Inform. Control 8 (1965), 338-353. Zbl 0942.00007, |
| Reference:
|
[9] Zadeh, L. A.: Similarity relations and fuzzy orderings..Inform. Sci. 3 (1971), 177-200. |
| Reference:
|
[10] Zhang, H.-P., Pérez-Fernández, R., Beats, B. De: Fuzzy betweenness relations and their connection with fuzzy order relations..Fuzzy Sets Systems 384 (2020), 1-22. |
| . |
