An approach toward defining L-fuzzy lattices

The paper deals with one possible approach that can be used in the process of defining lattice valued fuzzy lattice (L-fuzzy lattice). The idea of fuzzification of the ordering of a crisp lattice to obtain a weakly reflexive lattice valued ordering relation is developed in order to obtain a structure whose level sets are crisp lattices. At this point, two different treatments of the problem can be effectuated, and therefore two definitions of L-fuzzy lattices can be offered. The theorems for synthesis of those structures are also given, as well as an illustrating example.