Product of fuzzy \(H_v\)-subgroups. (English) Zbl 0957.20054

Since the concept of hypergroup was too restrictive [cf. H. X. Li, Q. Z. Duan, P. Z. Wang, BUSEFAL 23, 22-28 (1985; Zbl 0582.20063); H. X. Li, P. Z. Wang, ibid. 25, 8-11 (1986; Zbl 0589.20055); Z. L. Zhang, ibid. 31, 92-94 (1987; Zbl 0631.20021)] there were introduced weaker models of algebraic structures in a subset family as grey groups [cf. Q. Z. Xu, J. Grey Syst. 5, No. 1, 57-64 (1993; Zbl 0791.20092)] and \(H_v\)-groups [cf. T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, Florida (1994; Zbl 0828.20076)]. Fuzzy \(H_v\)-groups were introduced by the author [cf. Fuzzy Sets Syst. 101, No. 1, 191-195 (1999; Zbl 0935.20065)]. This paper examines products and quotient structures of fuzzy \(H_v\)-groups with respect to triangular norms [cf. H. Sherwood, Fuzzy sets Syst. 11, 79-89 (1983; Zbl 0529.20021)].


20N25 Fuzzy groups
20N20 Hypergroups