Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices

Autor: Berhanu Assaye Alaba, Wondwosen Zemene Norahun
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Advances in Fuzzy Systems, Vol 2019 (2019)
Druh dokumentu: article
ISSN: 1687-7101
1687-711X
DOI: 10.1155/2019/4263923
Popis: In this paper, we introduce the concept of kernel fuzzy ideals and ⁎-fuzzy filters of a pseudocomplemented semilattice and investigate some of their properties. We observe that every fuzzy ideal cannot be a kernel of a ⁎-fuzzy congruence and we give necessary and sufficient conditions for a fuzzy ideal to be a kernel of a ⁎-fuzzy congruence. On the other hand, we show that every fuzzy filter is the cokernel of a ⁎-fuzzy congruence. Finally, we prove that the class of ⁎-fuzzy filters forms a complete lattice that is isomorphic to the lattice of kernel fuzzy ideals.
Databáze: Directory of Open Access Journals
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