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Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

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Abstract

This paper considers the relationships among L-fuzzy sets, rough sets and n-ary hypergroup theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy n-ary subhypergroups of a commutative n-ary hypergroup is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy n-ary subhypergroup are introduced and studied. Then, a new algebraic structure called (invertible) L-fuzzy rough n-ary subhypergroups is defined, and the (strong) homomorphism of lower and upper L-fuzzy rough approximation operators is studied.

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Acknowledgments

The authors 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 research was supported by National Natural Science Foundation of China (60774049; 60875034;90818025); the Natural Science Foundation of Education Committee of Hubei Province, China (D20092901; Q20092907; D20082903; B200529001) and the Natural Science Foundation of Hubei Province, China (2008CDB341).

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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 Institute for Nationalities, 445000, Enshi, Hubei Province, China

    Jianming Zhan

  3. Department of Biology and Agro-Industrial Economy, Via delle Scienze 208, 33100, Udine, Italy

    P. Corsini

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  1. Yunqiang Yin
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  2. Jianming Zhan
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  3. P. Corsini
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Correspondence to Yunqiang Yin.

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Yin, Y., Zhan, J. & Corsini, P. Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice. Neural Comput & Applic 20, 41–57 (2011). https://doi.org/10.1007/s00521-010-0465-6

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  • DOI: https://doi.org/10.1007/s00521-010-0465-6

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