Khan, Asghar; Muhammad, Shakoor; Khalaf, Mohammed M. More general forms of \((\in, \in \vee Q_k)\) fuzzy filters of ordered semigroups. (English) Zbl 1372.06008 Honam Math. J. 39, No. 2, 199-216 (2017). 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. Cited in 2 Documents MSC: 06F05 Ordered semigroups and monoids 20M12 Ideal theory for semigroups 03G25 Other algebras related to logic Keywords:fuzzy left filter; fuzzy right filter; \({(\in,\in \vee q)}\)-fuzzy filters; \({(\in,\in \vee q_k)}\)-fuzzy filter; \({(\in,\in \vee q_k^{\delta})}\)-fuzzy filter Citations:Zbl 1296.06011 PDFBibTeX XMLCite \textit{A. Khan} et al., Honam Math. J. 39, No. 2, 199--216 (2017; Zbl 1372.06008) Full Text: DOI