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New types of fuzzy ideals of near-rings

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Abstract

In this paper, we consider the \((\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})\)-fuzzy and \((\overline{\in}_{\gamma},\overline{\in}_{\gamma} \vee \; \overline{\hbox{q}}_{\delta})\)-fuzzy subnear-rings (ideals) of a near-ring. Some new characterizations are also given. In particular, we introduce the concepts of (strong) prime \((\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})\)-fuzzy ideals of near-rings and discuss the relationship between strong prime \((\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})\)-fuzzy ideals and prime \((\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})\)-fuzzy ideals of near-rings.

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Acknowledgments

Supported by the National Natural Science Foundation of China (60875034); the Innovation Term of Education Committee of Hubei Province, China (T201109) and the Natural Science Foundation of Hubei Province, China (2009CDB340).

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Authors and Affiliations

  1. Department of Mathematics, Hubei University for Nationalities, Enshi, 445000, China

    Jianming Zhan

  2. School of Mathematics and Information Sciences, East China Institute of Technology, Fuzhou, Jiangxi, 344000, China

    Yunqiang Yin

Authors
  1. Jianming Zhan
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  2. Yunqiang Yin
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Correspondence to Jianming Zhan.

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Zhan, J., Yin, Y. New types of fuzzy ideals of near-rings. Neural Comput & Applic 21, 863–868 (2012). https://doi.org/10.1007/s00521-011-0570-1

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  • DOI: https://doi.org/10.1007/s00521-011-0570-1

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