Filters of ordered semigroups based on the fuzzy points

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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