Linear Diophantine fuzzy ideal theory in d-algebras

Abstract

This study presents a comprehensive investigation into the integration of linear Diophantine fuzzy sets within the framework of $d$-algebraic structures, offering a refined perspective on the interaction between fuzzy logic and abstract algebra. The concepts of (weak) linear Diophantine fuzzy $d$-subalgebras and (weak) linear Diophantine fuzzy $d$-ideals are rigorously
defined and formalized, supported by illustrative examples to enhance conceptual clarity. A thorough examination is conducted to identify and characterize the algebraic properties of these structures, with a particular focus on establishing the necessary and sufficient conditions under which a structural transformation between the two notions is feasible. Furthermore, the study delves into two distinguished classes of ideals in $d$-algebras through the lens of linear Diophantine fuzzy theory, emphasizing their structural alignment and interaction with classical $d$-ideals.