Fuzzy Lattices

A genera1 development of the theory of fuzzy sublattices is provided in the paper. Several characterizations of a fuzzy sublattice, fuzzy idea1 (dual ideal), and fuzzy prime idea1 (dual ideal) are obtained. Structural theorems for fuzzy sublattices, fuzzy ideals (dual ideals) generated by a fuzzy set are proved. Moreover, the notion of fuzzy convex sublattice is introduced and discussed. Various fuzzy analogs of the results of classical lattice theory are established.