Proposition 2 J

Corsini has dened a hyperoperation through a fuzzy set and has shown to be a join hyper-operation. This hyperoperation can be generalized so that it can be dened in terms of an L-fuzzy set. We explore the generalized hyperoperation and give suÆcient conditions for the resulting hy-perstructure to be a hypergroup and / or a join space. AMS Classication: 06B99, 06D30, 08A72, 20N20. In [3] Corsini used a fuzzy set to dene a hyperoperation and showed that it is a join hyperop-eration. This hyperoperation was further studied by Corsini in [4] and by Ameri and Zahedi in [1]. It is easy to generalize Corsini's hyperoperation so that it can be dened in terms of an L-fuzzy set. In this paper we explore the generalized hyperoperation and give suÆcient conditions for the resulting hyperstructure to be a hypergroup and / or a join space. For the purposes of this paper, an L-fuzzy set is a function from any set to a complete lattice (for more details on L-fuzzy sets see [7]). The notions of hypergroup and join space is described in [2]. The following will remain xed for the remainder of the paper: X is a set; P(X) denotes the power set of X; (L;) is a complete lattice; M: X! L is an L-fuzzy set; M(X) is the image of X under M. De nition 1 We dene the relationship J