Corsini, P., Cristea, I. (2004). FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7. Iranian Journal of Fuzzy Systems, 1(2), 15-32. doi: 10.22111/ijfs.2004.499
Piergiulio Corsini; Irina Cristea. "FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7". Iranian Journal of Fuzzy Systems, 1, 2, 2004, 15-32. doi: 10.22111/ijfs.2004.499
Corsini, P., Cristea, I. (2004). 'FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7', Iranian Journal of Fuzzy Systems, 1(2), pp. 15-32. doi: 10.22111/ijfs.2004.499
Corsini, P., Cristea, I. FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7. Iranian Journal of Fuzzy Systems, 2004; 1(2): 15-32. doi: 10.22111/ijfs.2004.499
i.p.s. hypergroups are canonical hypergroups such that $[\forall(a,x),a+x\ni x]\Longrightarrow[a+x=x].$ i.p.s. hypergroups were investigated in [1], [2], [3], [4] and it was proved that if the order is less than 9, they are strongly canonical (see [13]). In this paper we obtain the sequences of fuzzy sets and of join spaces determined (see [8]) by all i.p.s. hypergroups of order seven. For the meaning of the hypergroups iH and the notations, see [7], [8].
[1] P. Corsini, Sugli ipergruppi canonici finiti con identit`a parziali scalari, Rend. Circolo Mat. di Palermo, Serie II, Tomo XXXVI (1987). [2] P. Corsini, (i.p.s.) Ipergruppi di ordine 6, Ann. Sc. de l’Univ. Blaise Pascal, Clermont–Ferrand II (1987). [3] P. Corsini, (i.p.s.) Ipergruppi di ordine 7, Atti Sem. Mat. Fis. Univ. Modena, XXXIV (1985–1986). [4] P. Corsini, (i.p.s.) Hypergroups of order 8, Aviani Editore (1989) 1–106.
[5] P. Corsini, Prolegomena of hypergroups, Aviani Editore (1993). [6] P. Corsini, On W–hypergroups, Proceedings of I.R.B. InternationalWorkshops, New Frontiers in Multivalued Hyperstructures, Monteroduni (1995). [7] P. Corsini, Join spaces, power sets, fuzzy sets, Proceedings of the Fifth International Congress on Algebraic Hyperstructures and Applications, 1993, Ia¸si, Hadronic Press (1994). [8] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. of Math. SEAMS, 27 (2003). [9] P. Corsini and I. Cristea, Fuzzy grade of i.p.s. hypergroups of order less or equal to 6, accepted by PU.M.A., Budapest (2004). [10] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. of Combinatorics, Information and System Sciences, 20 (1) (1995). [11] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Math., Kluwer Academic Publishers (2003). [12] J. Mittas, Hypergroupes canoniques, Math. Balkanica, 2 (1972). [13] J. Mittas, Hypergroupes canoniques, values et hypervalues. hypergroupes fortement et sup´erieurement canoniques, Math. Balk., 8 (1978). [14] W. Prenowitz and J. Jantosciak, Geometries and join spaces, J. reine und angewandte Math., 257 (1972) 100–128. [15] L. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353.
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