H‐Fuzzy Ideals and H‐Fuzzy Filters in Distributive Join‐Semilattices

This paper investigates ‐fuzzy ideals of distributive join‐semilattices with least element 0 whose codomain is a complete lattice that satisfies the infinite meet distributive law. We also construct a number of characterizations for any ‐fuzzy ideal generated by an ‐fuzzy subset. It is also proved that the class of all ‐fuzzy ideals of any distributive join‐semilattice with 0 is a complete lattice and forms an algebraic closure ‐fuzzy set system. We also introduce the concept of ‐valued weights over a distributive join‐semilattice with 0, and we derive a lattice isomorphism between the class of all ‐fuzzy ideals of any distributive join‐semilattice with 0 and the lattice of all ‐valued weights over it. The concept of ‐fuzzy filters of distributive join‐semilattices with 0 is presented, and it is characterized using level sets.