fuzzy filter
Open AccessArticle
Fuzzy Filters in Ordered Semirings
Annals of Communications in Mathematics 2024
, 7 (2)
, 114-127
DOI: https://doi.org/10.62072/acm.2024.070205
AbstractWe introduce the notion of ideal, prime ideal, filter, fuzzy ideal, fuzzy prime ideal, fuzzy filter of an ordered semiring and study their properties and relations between them. We characterize the prime ideals and filters of an ordered semiring with respect to fuzzy ideals and fuzzy filters respectively. We proved a fuzzy subset µ is a fuzzy filter of an ordered semiring M if and only if µMT β, : X → [0, 1] is a fuzzy filter of an ordered semiring M. M and N be ordered semirings and ϕ : M → N be an onto homomorphism. If f is a ϕ homomorphism invariant fuzzy filter of M then ϕ(f) is a fuzzy filter of N.