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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:
16Y99Generalizations of associative rings and algebras
20N20Hypergroups (group theory)
08A72Fuzzy algebraic structures
References:
[1]Ameri, R.; Zahedi, M. M.: Fuzzy subhypermodules over fuzzy hyperrings, , 1-14 (1996) · 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) · Zbl 0785.20032
[4]Corsini, P.: Join spaces, power sets, fuzzy sets, , 45-52 (1994) · Zbl 0847.20065
[5]Corsini, P.: Fuzzy sets, join spaces and factor spaces, Pure math. Appl. 11, No. 3, 439-446 (2000) · Zbl 0980.20071
[6]Corsini, P.; Leoreanu, V.: Applications of hyperstructure theory, Advances in mathematics 5 (2003) · 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 · doi:10.1007/BF02871859
[8]Corsini, P.; Leoreanu, V.: Join spaces associated with fuzzy sets, J. combinatorics inf. Syst. sci. 20, No. 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 hv-groups, Fuzzy sets syst. 101, 191-195 (1999) · Zbl 0935.20065 · doi:10.1016/S0165-0114(97)00071-7
[11]Davvaz, B.: Fuzzy hv submodules, Fuzzy sets syst. 117, 477-484 (2001) · Zbl 0974.16041 · doi:10.1016/S0165-0114(98)00366-2
[12]Davvaz, B.; Corsini, P.: Generalized fuzzy sub-hyperquasigroups of hyperquasigroups, Soft comput. 10, No. 11, 1109-1114 (2006) · Zbl 1106.20055 · doi:10.1007/s00500-006-0048-8
[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)
[15]Kehagias, Ath.: An example of L-fuzzy join space, Rendiconti di circolo matematico di Palermo 52, 322-350 (2003)
[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.
[19]Leoreanu-Fotea, V.; Davvaz, B.: N-hypergroups and binary relations, Eur. J. Combinatorics 29, 1207-1218 (2008) · Zbl 1179.20070 · doi:10.1016/j.ejc.2007.06.025
[20]F. Marty, Sur une généralisation de la notion de group, in: 4th Congress Math. Scandinaves, Stockholm, 1934, pp. 45 – 49. · Zbl 61.1014.03
[21]Mordeson, J. N.; Malik, M. S.: Fuzzy commutative algebra, (1998)
[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)
[25]Rosenfeld, A.: Fuzzy groups, J. math. Anal. appl. 35, 512-517 (1971) · Zbl 0194.05501 · doi:10.1016/0022-247X(71)90199-5
[26]M.K. Sen, R. Ameri, G. Chowdhury, Fuzzy hypersemigroups, Soft Comput. (2007), doi: http://10.1007/s00500-007-0257-9.
[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) · 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