| Title:
|
Characterizations of sub-semihypergroups by various triangular norms (English) |
| Author:
|
Davvaz, B. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
923-932 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the structure and properties of $TL$-sub-semihypergroups, where $T$ is an arbitrary triangular norm on a given complete lattice $L$. We study its structure under the direct product and with respect to the fundamental relation. In particular, we consider $L=[0,1]$ and $T=\min $, and investigate the connection between $TL$-sub-semihypergroups and the probability space. (English) |
| Keyword:
|
semihypergroup |
| Keyword:
|
complete lattice |
| Keyword:
|
triangular norm |
| Keyword:
|
fundamental relation |
| Keyword:
|
probability space |
| MSC:
|
20N20 |
| idZBL:
|
Zbl 1081.20079 |
| idMR:
|
MR2184373 |
| . |
| Date available:
|
2009-09-24T11:29:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128034 |
| . |
| Reference:
|
[1] M. Akgul: Some properties of fuzzy groups.J. Math. Anal. Appl. 133 (1998), 93–100. MR 0949320 |
| Reference:
|
[2] J. M. Anthony and H. Sherwood: Fuzzy groups redefined.J. Math. Anal. Appl. 69 (1979), 124–130. MR 0535285, 10.1016/0022-247X(79)90182-3 |
| Reference:
|
[3] G. Birkhoff: Lattice Theory.American Mathematical Society, Collequium Publications, Vol. 25, 1979. Zbl 0505.06001, MR 0598630 |
| Reference:
|
[4] P. Corsini: Prolegomena of Hypergroup Theory, second edition.Aviani Editor, 1993. MR 1237639 |
| Reference:
|
[5] B. Davvaz: Product of fuzzy $H_v$-subgroups.Fuzzy Math. 8 (2000), 43–51. Zbl 0957.20054, MR 1750241 |
| Reference:
|
[6] B. Davvaz: $TL$-subpolygroups of a polygroup.Pure Math. Appl. 12 (2001), 137–145. Zbl 1004.20056, MR 1905125 |
| Reference:
|
[7] B. Davvaz: Interval-values fuzzy subhypergroups.Korean J. Comput. Appl. Math. 6 (1999), 197–202. MR 1669606, 10.1007/BF02941917 |
| Reference:
|
[8] B. Davvaz: Fuzzy $H_v$-groups.Fuzzy sets and systems 101 (1999), 191–195. Zbl 0935.20065, MR 1658991 |
| Reference:
|
[9] B. Davvaz: Fuzzy hyperideals in semihypergroups.Italian J. Pure Appl. Math. 8 (2000), 67–74. Zbl 1097.20524, MR 1793744 |
| Reference:
|
[10] J. A. Goguen: $L$-fuzzy sets.J. Math. Anal. Appl. 18 (1967), 145–174. Zbl 0145.24404, MR 0224391, 10.1016/0022-247X(67)90189-8 |
| Reference:
|
[11] Young Bae Jun, Eun Hwan Roh and Hee Sik Kim: On fuzzy $B$-algebras.Czechoslovak Math. J. 52(127) (2002), 375–384. MR 1905445, 10.1023/A:1021739030890 |
| Reference:
|
[12] Young Bae Jun, J. Neggers and Hee Sik Kim: On $L$-fuzzy ideals in semirings I.Czechoslovak Math. J. 48(123) (1998), 669–675. MR 1658233, 10.1023/A:1022479320940 |
| Reference:
|
[13] F. Marty: Sur une généralisation de la notion de groupe.Proceedings of the 8th Congress Math. Scandenaves, Stockholm, 1935, pp. 45–49. Zbl 0012.05303 |
| Reference:
|
[14] J. Neggers, Young Bae Jun and Hee Sik Kim: On $L$-fuzzy ideals in semi-rings II.Czechoslovak Math. J. 49(124) (1999), 127–133. MR 1676825, 10.1023/A:1022416410366 |
| Reference:
|
[15] V. V. Negoita and D. A. Ralescu: Applications of Fuzzy Sets System Analysis.Birkhäuser-Verlag, Basel, 1975. MR 0490083 |
| Reference:
|
[16] A. Rosenfeld: Fuzzy groups.J. Math. Anal. Appl. 35 (1971), 512–517. Zbl 0194.05501, MR 0280636, 10.1016/0022-247X(71)90199-5 |
| Reference:
|
[17] B. Schweizer and A. Sklar: Statistical metric spaces.Pacific J. Math, 10 (1960), 313–334. MR 0115153, 10.2140/pjm.1960.10.313 |
| Reference:
|
[18] T. Vougiouklis: Hyperstructures and Their Representations.Hadronic Press, Palm Harber, 1994. Zbl 0828.20076, MR 1270451 |
| Reference:
|
[19] Xue-hai Yuan and E. Stanly Lee: A fuzzy algebraic system based on the theory of falling shadows.J. Math. Anal. Appl. 208 (1997), 243–251. MR 1440354, 10.1006/jmaa.1997.5331 |
| Reference:
|
[20] L. A. Zadeh: Fuzzy sets.Inform. Control 8 (1965), 338–353. Zbl 0139.24606, MR 0219427, 10.1016/S0019-9958(65)90241-X |
| . |
