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More general forms of \((\in, \in \vee Q_k)\) fuzzy filters of ordered semigroups. (English) Zbl 1372.06008

Summary: In the paper [J. Intell. Fuzzy Syst. 24, No. 3, 619–630 (2013; Zbl 1296.06011)], Y. B. Jun et al. discussed the notion of \((\in,\in \vee q_k)\)-fuzzy left (resp., right) filters as a generalization of the notion of \((\in,\in \vee q)\)-fuzzy left (resp., right) filters of ordered semigroups. In this article, we try to obtain a more general form that \((\in,\in \vee q_k)\)-fuzzy left (resp., right) filters in ordered semigroups. The notion of \((\in,\in \vee q_k^{\delta})\)-fuzzy left (resp., right) filters is discussed, and several properties are investigated. Characterizations of an \((\in,\in \vee q_k^{\delta})\)-fuzzy left (resp., right) filter are established. A condition for an \((\in,\in \vee q_k^{\delta})\)-fuzzy left (resp., right) filter to be a fuzzy left (resp., right) filter is provided. The important achievement of the study with an \((\in,\in \vee q_k^{\delta})\)-fuzzy left (right) filter is that the notion of an \((\in,\in \vee q_k)\)-fuzzy left ( right) filter and hence an \((\in,\in \vee q)\)-fuzzy left (resp. right) filter are special cases of an \((\in,\in \vee q_k^{\delta})\)-fuzzy left (resp. right) filter, and thus several results in published papers are becoming corollaries of our results obtained in this paper.

MSC:

06F05 Ordered semigroups and monoids
20M12 Ideal theory for semigroups
03G25 Other algebras related to logic

Citations:

Zbl 1296.06011
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