Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras

Abstract

In this paper, we apply the concept of linear Diophantine fuzzy sets in 𝐵𝐶𝐾/𝐵𝐶𝐼-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained.

Keywords: BCI-algebra; BCK-algebra; linear Diophantine fuzzy set (LDFS); LDF-subalgebra; LDF-ideal; LDF-commutative ideal