Linear Diophantine fuzzy substructures of ordered semigroups

Abstract

As an extension of the fuzzy set, linear Diophantine fuzzy set (LDFS) was recently introduced. In this paper, we apply the concept of LDFS in ordered semigroups by introducing some new related concepts. More precisely, we study LDF-ideals and LDF-interior ideals of ordered semigroups, illustrate non-trivial examples on each, and present some of their properties. Finally, and using LDFS, we discuss the simplicity of an ordered semigroup.

Keywords 06D72, 06F05, 08A72, LDF-ideal, LDF-interior ideal, LDF-simple, LDF-subsemigroup, Level set, Linear Diophantine fuzzy set (LDFS), Ordered semigroup