Linear Diophantine fuzzy subsets of polygroups

Abstract

Linear Diophantine fuzzy sets were recently introduced as a generalized form of fuzzy sets. The aim of this paper is to shed the light on the relationship between algebraic hyperstructures and linear Diophantine fuzzy sets through polygroups. More precisely, we introduce the concepts of linear Diophantine fuzzy subpolygroups of a polygroup, linear Diophantine fuzzy normal subpolygroups of a polygroup, and linear Diophantine anti-fuzzy subpolygroups of a polygroup. Furthermore, we study some of their properties and characterize them in relation to level and ceiling sets.

Keywords

• polygroup
• linear diophantine fuzzy set
• linear diophantine fuzzy subpolygroup
• linear diophantine fuzzy normal subpolygroup
• level set
• linear diophantine anti-fuzzy subpolygroup
• ceiling set