Linear Diophantine fuzzy BE-algebras

With the intention of applying linear Diophantine fuzzy sets to (logical) algebraic structures, in particular BE-algebra, the concept of weak linear Diophantine fuzzy BE-algebras is introduced, and its related properties are investigated. The conditions for the weak linear Diophantine fuzzy set to be a weak linear Diophantine fuzzy BE-algebra are explored. The role of reference parameters is given in the process that weak linear Diophantine level sets of a weak linear Diophantine fuzzy BE-algebra become subalgebras. The homomorphic preimage and image of a weak linear Diophantine fuzzy BE-algebra are proven to be weak linear Diophantine fuzzy BE-algebras. A new weak linear Diophantine fuzzy set consists of a combination of a given weak linear Diophantine fuzzy set and homomorphism, and then the relationship between a given weak linear Diophantine fuzzy set and a new weak linear Diophantine fuzzy set for the possibility of weak linear Diophantine fuzzy BE-algebra are explored.