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Soft hyperstructure. (English) Zbl 1228.03035

Summary: We study soft hypergroupoids. Firstly, we introduce the notion of soft hypergroupoids, and some examples are given. Also, we show that soft hypergroupoids are closely related to \(L\)-subhypergroupoid. Secondly, using the notion of soft hypergroupoid, some new properties of soft hypergroupoids are obtained. Lastly, we investigate some properties of soft subhypergroupoids.

MSC:

03E72 Theory of fuzzy sets, etc.
08A72 Fuzzy algebraic structures
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[1] F. Marty, Sur une generalization de la notion de group, in: Proc. 8th Congress Mathematics Scandenaves, Stockholm, (1934) 45-49.
[2] P. Corsini, Prolegomena of hypergroup theory, second edition, Aviani editor, 1993. · Zbl 0785.20032
[3] Corsini, P.; Leoreanu, V., Applications of hyperstructures theory, advanced in mathematics, (2003), Kluwer Academic Publisher
[4] Davvaz, B.; Leoreanu-Fotea, V., Hyperring theory and applications, (2007), International Academic Press USA · Zbl 1204.16033
[5] Vougiouklis, T., Hyperstructures and their representations, (1994), Hadronic Press Florida · Zbl 0828.20076
[6] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
[7] Pawlak, Z., Rough sets, Int. J. comput. inform. sci., 11, 341-356, (1982) · Zbl 0501.68053
[8] Molodtsov, D., Soft set theory first results, Comput. math. appl., 37, 19-31, (1999) · Zbl 0936.03049
[9] Maji, P.K.; Roy, A.R.; Biswas, R., An application of soft sets in a decision making problem, Comput. math. appl., 44, 1077-1083, (2002) · Zbl 1044.90042
[10] Pei, D.W.; Miao, D., From soft sets to information systems, IEEE international conference on granular computing, 617-621, (2005)
[11] Roy, A.R.; Maji, P.K., A fuzzy soft set theoretic approach to decision making problems, J. comput. appl. math., 203, 412-418, (2007) · Zbl 1128.90536
[12] Maji, P.K.; Biswas, R.; Roy, A.R., Soft set theory, Comput. math. appl., 45, 555-562, (2003) · Zbl 1032.03525
[13] Ali, M.I.; Feng, F.; Liub, X.; Minc, W.K.; Shabir, M., On some new operations in soft set theory, Comput. math. appl., 57, 1547-1553, (2009) · Zbl 1186.03068
[14] Aktaş, H.; Çağman, N., Soft sets and soft groups, Inform. sci., 177, 2726-2735, (2007) · Zbl 1119.03050
[15] Jun, Y.B., Soft BCK/BCI-algebras, Comput. math. appl., 56, 1408-1413, (2008) · Zbl 1155.06301
[16] Jun, Y.B.; Park, C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. sci., 178, 2466-2475, (2008) · Zbl 1184.06014
[17] Feng, F.; Jun, Y.B.; Zhao, X., Soft semirings, Comput. math. appl., 56, 2621-2628, (2008) · Zbl 1165.16307
[18] Çelik, Y.; Ekiz, C.; Yamak, S., A new view on soft rings, Hacettepe journal of mathematics and statistics, 40, 273-286, (2011) · Zbl 1231.16040
[19] Yang, C.-F., Fuzzy soft semigroups and fuzzy soft ideals, Comput. math. appl., 61, 255-261, (2010) · Zbl 1211.20074
[20] Goguen, J.A., \(L\)-fuzzy sets, J. math. anal. appl., 18, 145-174, (1967) · Zbl 0145.24404
[21] Wu, W.-Z.; Mi, J.-S.; Zhang, W.-X., Generalized fuzzy rough sets, Inform. sci., 151, 263-282, (2003) · Zbl 1019.03037
[22] Kazancı, O.; Yılmaz, Ş.; Yamak, S., Soft sets and soft \(B C H\)-algebras, Hacettepe J. math. statistics, 39, 205-217, (2010) · Zbl 1203.06022
[23] Rosenfeld, A., Fuzzy groups, J. math. anal. appl., 35, 512 517-512 517, (1971) · Zbl 0194.05501
[24] Ameri, R.; Zahedi, M.M., Hyperalgebraic system, Italian J. pure appl. math., 6, 21-32, (1999) · Zbl 0959.20061
[25] Corsini, P., Join spaces, power sets, fuzzy sets, () · Zbl 0847.20065
[26] Davvaz, B., Fuzzy \(H_v\)-groups, Fuzzy sets syst., 101, 191-195, (1999) · Zbl 0935.20065
[27] Zahedi, M.M.; Bolurian, M.; Hasankhani, A., On polygroups and fuzzy subpolygroups, J. fuzzy math., 3, 1-15, (1995) · Zbl 0854.20073
[28] Davvaz, B., \(T_H\) and \(S_H\)- interval-valued fuzzy \(H_v\) subgroups, Indian J. pure appl. math., 35, 1, 61-69, (2004) · Zbl 1051.20042
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