CLOSURE SYSTEMS OVER GENERALIZED RESIDUATED LATTICES

Abstract

The present paper is an attempt to introduce the closure system over generalized residuated lattices the residuated lattices in which the multiplication operator is not necessarily commutative. Different closure operators and their corresponding systems depending on the type of meet operation and two implication operators are defined. In the present paper, the least closure system including the introduced closure systems is obtained and an Algorithm is presented to calculate this closure system. Three different closure system and the unique bases for these specific closure systems and the relationships among them are also introduced, then six different Algorithms that are non-comparable in terms of set inclusion and represent non-redundant sets of generators are presented.