Implicative Almost Distributive Lattice

In this paper, we introduce the concept of Implicative Almost Distributive Lattices (IADLs) as a generalization of implicative algebra in the class of Almost Distributive Lattices. We discuss some properties of IADL and derive some equivalent conditions in IADLs. We also discuss some characterizations of IADL to become an implicative algebra

Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

In this paper, we introduce the concept of transitive and absorbent filters of implicative almost distributive lattices and studied their properties. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. A set of equivalent conditions is obtained for a filter to become an absorbent filter

Weak LI-ideals in implicative almost distributive lattices

In the field of many valued logic, lattice valued logic (especially ideals) plays an important role. Nowadays, lattice valued logic is becoming a research area. Researchers introduced weak LI-ideals of lattice implication algebra. Furthermore, other scholars researched LI-ideals of implicative almost distributive lattice. Therefore, the target of this paper was to investigate new development on the extension of LI-ideal theories and properties in implicative almost distributive lattice. So, in this paper, the notion of weak LI-ideals and maximal weak LI- ideals of implicative almost distributive lattice are defined. The properties of weak LI- ideals in implicative almost distributive lattice are studied and several characterizations of weak LI-ideals are given. Relationship between weak LI-ideals and weak filters are explored. Hence, the extension properties of weak LI-ideal of lattice implication algebra to that of weak LI-ideal of implicative almost distributive lattice were shown