On the Definition of the Fuzzy Sublattice

In this paper, we present two approaches to define fuzzy sublattice. Firstly, by the use of the relations between fuzzy points and fuzzy subsets, definition of (szligmacr,alphamacr) fuzzy sublattice is given. We have shown that the acceptable non-trival concepts obtained in this manner are the (isin,isin)-fuzzy sublattice, (isin,isinnuq)-fuzzy sublattice and (isinmacr,isinmacrnuqmacr)-fuzzy sublattice. Secondly, based on the theory of a consensus space presents by Hisakichi Suzuki, concept of C-fuzzy sublattice is acquired. It is pointed that (isin,isin)-fuzzy sublattice is C-fuzzy sublattice and C-fuzzy sublattice is defined on a t-norm. Finally, it is proved that C-fuzzy sublattice is isomorphic to C-fuzzy sublattice generated by a sublattice L.