Affiliations: Department of Mathematics Education, RINS Gyeongsang National University, Chinju, Korea | Department of Mathematics, Yazd University, Yazd, Iran | Department of Mathematics, COMSATS Institute of Information Technology KPK, Abbottabad, Pakistan
Note: [] Corresponding author. Asghar Khan, Department of Mathematics, COMSATS Institute of Information Technology KPK, Abbottabad, Pakistan. Tel.: +92 331 5479017; E-mails: [email protected] (Asghar Khan), [email protected] (Young Bae Jun), [email protected] (Bijan Davvaz).
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.
Keywords: Fuzzy left (right) filter, (∈, ∈ ∨ q)-fuzzy left (right) filter, (∈, ∈ ∨ $q_k$)-fuzzy left (right) filter, fuzzifying left (right) filter, t-implication-based fuzzy left (right) filter
