FILTERS THEORY OF SMARANDACHE RESIDUATED LATTICE

Residuated lattices play an important role in the study of fuzzy logic and filters are basic concepts in residuated lattices and other algebraic structures. The aim of this paper is to introduce a Smarandache B-L-residuated lattice. Then we define the notions of B-L-Smarandache deductive systems and B-L-Smarandache filters and investigate the relations among them. It is proved that every B-L-Smarandache filter is a B-L-Smarandache deductive system, but the converse may not be true, while filters and deductive systems are equivalent in the most of algebraic structures. Finally we introduce the concept of B-L-Smarandache implicative, positive implicative and fantastic filters and obtain some relationships between them.