Affiliations: [a] School of Mathematics and Computer, Wuyi University, Wuyishan, Fujian, China | [b] Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Republic of Korea
Correspondence:
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Corresponding author. Hee Sik Kim, Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea. Tel.: +82 2 2220 0897; Fax: +82 2 2281 0019; E-mail: [email protected].
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, ∧-product, ∨-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.
