A Study of (a, b)-Fuzzy Sublattices and (a, b)-Fuzzy Ideals of Distributive Lattices

The framework of fuzzy algebraic structures is extended to distributive lattices through the introduction and investigation of (a, b)-fuzzy sublattices and (a, b)-fuzzy ideals. Building on foundational work by Zadeh, Rosenfeld, Liu, Sharma, Yuan, Wu, and S. K. Nimbhorkar, this study generalises the perception of (a, b)-fuzzy subrings and (a, b)-fuzzy ideals from ring theory to lattice theory. The paper recalls key definitions and properties of fuzzy subsets in distributive lattices with least and greatest elements to provide the necessary preliminaries. Subsequently, (a, b)-fuzzy sublattices and (a, b)-fuzzy ideals are formally defined, their fundamental properties are investigated, and their relationships with classical fuzzy sublattices and fuzzy ideals are explored. This generalisation offers new perspectives and analytical tools for studying fuzziness in lattice-theoretic contexts.