Non-commutative residuated lattices based on soft sets

Abstract

Molodtsov introduced the concept of soft set as a new mathematical tool for dealing with uncertainties. Recently, Cagman and Enginoglu [16] provided new definitions and operations on soft set theory. The paper applies new definitions and operations of soft sets to non-commutative residuated lattices. The notion of soft non-commutative residuated lattices is introduced. We give some specific examples to show the existence of soft non-commutative residuated lattices. The union, intersection, boolean AND-product, boolean OR-product and difference operations of soft non-commutative residuated lattices are investigated. Finally, we study the homomorphism properties of soft non-commutative residuated lattices. It is pointed out that the soft non-commutative residuated lattices are so general, all results in this paper also hold in most of soft non-commutative logic algebras and soft logic algebras.