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New types of fuzzy ideals of BCI-algebras

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Abstract

The concepts of \((\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})\)-fuzzy (p-, q- and a-) ideals and \((\overline{\in}_{\gamma},\overline{\in}_{\gamma} \! \vee\,{\rm \overline{q}}_{\delta})\)-fuzzy (p-, q- and a-) ideals in BCI-algebras are introduced. Some new characterizations are investigated. In particular, we prove that a fuzzy set μ of a BCI-algebra X is an \((\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})\)-fuzzy a-ideal of X if and only if it is both an \((\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})\)-fuzzy p-ideal and an \((\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})\)-fuzzy q-ideal.

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Acknowledgments

This research is partially supported by a grant of the National Natural Science Foundation of China (60875034); a grant of the Natural Science Foundation of Education Committee of Hubei Province, China (D20092901) and also the support of the Natural Science Foundation of Hubei Province, China (2009CDB340).

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Authors and Affiliations

  1. Department of Mathematics, Hubei Institute for Nationalities, 445000, Enshi, Hubei Province, People’s Republic of China

    Xueling Ma & Jianming Zhan

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

    Young Bae Jun

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  1. Xueling Ma
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  2. Jianming Zhan
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Correspondence to Jianming Zhan.

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Ma, X., Zhan, J. & Jun, Y.B. New types of fuzzy ideals of BCI-algebras. Neural Comput & Applic 21 (Suppl 1), 19–27 (2012). https://doi.org/10.1007/s00521-011-0558-x

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