Abstract

On a generalized deMorgan lattice (X, _<, V, A,') we introduce a family of join hyperoperations *p, parametrized by a parameter p X. As a result we obtain a family of join spaces (X, ,p). We show that: for every a, b X the family {a*p b}pex can be considered as the p-cuts of a L-fuzzy set a * b; in this manner we synthesize a L-fuzzy hyperoperation which takes pairs from X to L-fuzzy subsets of X. We then show that (X, ,p) is a L-fuzzy hypergroup (in the sense of Corsini) and can be considered as a L-fuzzy join space. Furthermore, a * b is a L-fuzzy interval for all a, b X.

Citations