Abstract
In the paper [B. Davvaz and A. Khan, Generalized fuzzy filters in ordered semigroups, IJST (2012) Vol. 36, A1: 77-86], Davvaz and Khan discussed the notion of (∈, ∈ ∨ q)-fuzzy left (right) filters as a generalization of the notion of fuzzy left (right) filters of ordered semigroups. In this article, we try to obtain a more general form than (∈, ∈ ∨ q)-fuzzy left (right) filters in ordered semigroups. The notion of an (∈, ∈ ∨ qk)-fuzzy left (right) filter is introduced, and several properties are investigated. Characterizations of an (∈, ∈ ∨ qk)-fuzzy left (right) filter are established. A condition for an (∈, ∈ ∨ qk)-fuzzy left (right) filter to be a fuzzy left (right) filter is provided. Using implication operators and the notion of implication-based fuzzy left (resp. right) filters, characterizations of a fuzzy left (resp. right) filter and an (∈, ∈ ∨ qk)-fuzzy left (resp. right) filter are considered.
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