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A new view of L-fuzzy polygroups

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Abstract

In this paper, we introduce the concept of (weak) L-fuzzy polygroups and give a theorem to present the connection between the crisp polygroups and L-fuzzy polygroups. We also provide the notion of (normal) L-fuzzy subpolygroups of a (weak) L-fuzzy polygroup and investigate some of their properties. We show that the set of all the normal L-fuzzy subpolygroups is a modular lattice and obtain a kind of weak L-fuzzy quotient polygroup. Moreover, we define two kinds of operators on \({\fancyscript{L}(H)}\), where \({\fancyscript{L}(H)}\) is the set of all the L-fuzzy subsets in a weak L-fuzzy polygroup H, to characterize L-fuzzy subpolygroups and present some related theorems. Finally, we investigate the homomorphism properties of L-fuzzy polygroups.

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Acknowledgments

We would like to express our warmest thanks to the referees for their interest in our work and their valuable comments for improving the paper. This work was supported by the Natural Science Foundation for Young Scholars of Jiangxi, China (2010GQS0003); the Science Foundation of Education Committee for Young Scholars of Jiangxi, China (GJJ11143); a grant of National Natural Science Foundation of China # 60875034; a grant of the Natural Science Foundation of Education Committee of Hubei Province, China, # D20092901; and also a grant of the Natural Science Foundation of Hubei Province, China # 2009CDB340.

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Authors and Affiliations

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

    Yunqiang Yin

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

    Jianming Zhan

  3. Department of Mathematics, Honghe University, 661100, Mengzi, Yunnan, China

    Xiaokun Huang

Authors
  1. Yunqiang Yin
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  2. Jianming Zhan
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  3. Xiaokun Huang
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Correspondence to Yunqiang Yin.

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Yin, Y., Zhan, J. & Huang, X. A new view of L-fuzzy polygroups. Neural Comput & Applic 20, 589–602 (2011). https://doi.org/10.1007/s00521-011-0555-0

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  • DOI: https://doi.org/10.1007/s00521-011-0555-0

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