An example of L-fuzzy join space

On a generalized deMorgan lattice (X, ≤, ∨, ∧,′) we introduce a family of join hyperoperations * p , parametrized by a parameterp eX. As a result we obtain a family of join spaces (X, * p ). We show that: for everya,b eX the family {a*pb} peX can be considered as thep-cuts of aL-fuzzy seta*b; in this manner we synthesize aL-fuzzy hyperoperation * which takes pairs fromX toL-fuzzy subsets ofX. We then show that (X, * p ) is aL-fuzzy hypergroup (in the sense of Corsini) and can be considered as aL-fuzzy join space. Furthermore,a*b is aL-fuzzy interval for alla,b eX.