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Ordered semigroups characterized by (\({ \in,\in \vee q}_{k}\))-fuzzy generalized bi-ideals

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Abstract

In this paper, we introduce a considerable machinery that permits us to characterize a number of special (fuzzy) subsets in ordered semigroups. In this regard, we generalize (Davvaz and Khan in Inform Sci 181:1759–1770 2011) and define (\(\in ,\in \vee q_{k}\))-fuzzy generalized bi-ideals in ordered semigroups, which is a generalization of the concept of an (α, β)-fuzzy generalized bi-ideal in an ordered semigroup. We also define (\(\in ,\in \vee q_{k}\))-fuzzy left (resp. right)-ideals. Using these concept, some characterization theorems of regular, left (resp. right) regular, completely regular and weakly regular ordered semigroups are provided. The upper/lower parts of an (\(\in ,\in \vee q_{k}\))-fuzzy generalized bi-ideal and (\(\in ,\in \vee q_{k}\))-fuzzy left (resp. right)-ideal are given, and some characterizations are provided.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Khyber Pukhtoon Khwa, Pakistan

    Asghar Khan

  2. Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, 660-701, Korea

    Young Bae Jun

  3. Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM, Johor Bahru, Johor, Malaysia

    Nor Haniza Sarmin & Faiz Muhammad Khan

Authors
  1. Asghar Khan
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  2. Young Bae Jun
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  3. Nor Haniza Sarmin
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  4. Faiz Muhammad Khan
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Correspondence to Asghar Khan.

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Khan, A., Jun, Y.B., Sarmin, N.H. et al. Ordered semigroups characterized by (\({ \in,\in \vee q}_{k}\))-fuzzy generalized bi-ideals. Neural Comput & Applic 21 (Suppl 1), 121–132 (2012). https://doi.org/10.1007/s00521-011-0731-2

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