×

zbMATH — the first resource for mathematics

Fuzzy hyperrings. (English) Zbl 1179.16029
Summary: We introduce and analyze the fuzzy hyperring notion. We consider and study the subfuzzy-structures of such a notion and homomorphisms between fuzzy hyperrings. Finally, fundamental relations on fuzzy hyperrings are analyzed. In all the paper, we follow a connection between hyperrings and fuzzy hyperrings.

MSC:
16Y99 Generalizations
20N20 Hypergroups
08A72 Fuzzy algebraic structures
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ameri, R.; Zahedi, M.M., Fuzzy subhypermodules over fuzzy hyperrings, (), 1-14 · Zbl 0883.16037
[2] Ameri, R.; Zahedi, M.M., Hypergroup and join spaces induced by a fuzzy subset, Pure math. appl., 8, 155-168, (1997) · Zbl 0905.20050
[3] Corsini, P., Prolegomena of hypergroup theory, (1993), Aviani Editore Italy · Zbl 0785.20032
[4] Corsini, P., Join spaces, power sets, fuzzy sets, (), 45-52 · Zbl 0847.20065
[5] Corsini, P., Fuzzy sets, join spaces and factor spaces, Pure math. appl., 11, 3, 439-446, (2000) · Zbl 0980.20071
[6] Corsini, P.; Leoreanu, V., Applications of hyperstructure theory, () · Zbl 1027.20051
[7] Corsini, P.; Leoreanu, V., Fuzzy sets and join spaces associated with rough sets, Rendiconti di circolo matematico di Palermo, 51, 527-536, (2002) · Zbl 1176.03035
[8] Corsini, P.; Leoreanu, V., Join spaces associated with fuzzy sets, J. combinatorics inf. syst. sci., 20, 1-4, 293-303, (1995) · Zbl 0887.20045
[9] Corsini, P.; Tofan, I., On fuzzy hypergroups, Pure math. appl., 8, 29-37, (1997) · Zbl 0906.20049
[10] Davvaz, B., Fuzzy \(H_v\)-groups, Fuzzy sets syst., 101, 191-195, (1999) · Zbl 0935.20065
[11] Davvaz, B., Fuzzy \(H_v\) submodules, Fuzzy sets syst., 117, 477-484, (2001) · Zbl 0974.16041
[12] Davvaz, B.; Corsini, P., Generalized fuzzy sub-hyperquasigroups of hyperquasigroups, Soft comput., 10, 11, 1109-1114, (2006) · Zbl 1106.20055
[13] Kaburlasos, V.G.; Petridis, V., Fuzzy lattice neurocomputing (FLN) models, Neural networks, 13, 1145-1170, (2000)
[14] Kehagias, Ath., L-fuzzy join and meet hyperoperations and the associated L-fuzzy hyperalgebras, Rendiconti di circolo matematico di Palermo, 51, 503-526, (2002) · Zbl 1072.06004
[15] Kehagias, Ath., An example of L-fuzzy join space, Rendiconti di circolo matematico di Palermo, 52, 322-350, (2003) · Zbl 1176.06006
[16] Leoreanu, V., Direct limit and inverse limit of join spaces associated with fuzzy sets, Pure math. appl., 11, 509-512, (2000) · Zbl 0980.20076
[17] V. Leoreanu, About hyperstructures associated with fuzzy sets of type 2, Ital. J. Pure Appl. Math. 17 (2005) 127-136. · Zbl 1150.20320
[18] V. Leoreanu-Fotea, B. Davvaz, Join \(n\)-spaces and lattices, Multiple Valued Logic Soft Comput. 15 (2008), accepted for publication. · Zbl 1179.20070
[19] Leoreanu-Fotea, V.; Davvaz, B., n-hypergroups and binary relations, Eur. J. combinatorics, 29, 1207-1218, (2008) · Zbl 1179.20070
[20] F. Marty, Sur une généralisation de la notion de group, in: \(4 \operatorname{th}\) Congress Math. Scandinaves, Stockholm, 1934, pp. 45-49.
[21] Mordeson, J.N.; Malik, M.S., Fuzzy commutative algebra, (1998), World Scientific Publishers · Zbl 1026.13002
[22] Petridis, V.; Kaburlasos, V.G., Fuzzy lattice neural network (FLNN): a hybrid model for learning, IEEE trans. neural networks, 9, 877-890, (1998)
[23] Petridis, V.; Kaburlasos, V.G., Learning in the framework of fuzzy lattices, IEEE trans. fuzzy syst., 7, 422-440, (1999)
[24] Prenowitz, W.; Jantosciak, J., Join geometries, (1979), Springer UTM · Zbl 0421.52001
[25] Rosenfeld, A., Fuzzy groups, J. math. anal. appl., 35, 512-517, (1971) · Zbl 0194.05501
[26] M.K. Sen, R. Ameri, G. Chowdhury, Fuzzy hypersemigroups, Soft Comput. (2007), doi: http://10.1007/s00500-007-0257-9. · Zbl 1142.20054
[27] Serafimidis, K.; Kehagias, A.; Konstantinidou, M., The L-fuzzy corsini join hyperoperation, Ital. J. pure appl. math., 12, 83-90, (2002) · Zbl 1138.20323
[28] Vougiouklis, T., Hyperstructures and their representations, (1994), Hadronic Press, Inc. · Zbl 0828.20076
[29] Zahedi, M.M.; Ameri, R., On the prime, primary and maximal subhypermodules, Ital. J. pure appl. math., 5, 61-80, (1999) · Zbl 0954.16034
[30] Zahedi, M.M.; Bolurian, M.; Hasankhani, A., On polygroups and fuzzy subpolygroups, J. fuzzy math., 3, 1-15, (1995) · Zbl 0854.20073
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.