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

Author

Listed:
  • Mohammed Amare Mohammed
  • Berehanu Bekele Belayneh
  • Zelalem Teshome Wale
  • Gezahagne Mulat Addis

Abstract

This paper investigates H-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 H-fuzzy ideal generated by an H-fuzzy subset. It is also proved that the class of all H-fuzzy ideals of any distributive join-semilattice with 0 is a complete lattice and forms an algebraic closure H-fuzzy set system. We also introduce the concept of H-valued weights over a distributive join-semilattice with 0, and we derive a lattice isomorphism between the class of all H-fuzzy ideals of any distributive join-semilattice with 0 and the lattice of all H-valued weights over it. The concept of H-fuzzy filters of distributive join-semilattices with 0 is presented, and it is characterized using level sets.

Suggested Citation

  • Mohammed Amare Mohammed & Berehanu Bekele Belayneh & Zelalem Teshome Wale & Gezahagne Mulat Addis, 2026. "H-Fuzzy Ideals and H-Fuzzy Filters in Distributive Join-Semilattices," Journal of Mathematics, Hindawi, vol. 2026, pages 1-10, March.
    • Handle: RePEc:hin:jjmath:2427855
    DOI: 10.1155/jom/2427855
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