Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice |
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| Authors: | Yunqiang Yin Jianming Zhan P Corsini |
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| Affiliation: | (1) School of Mathematics and Information Sciences, East China Institute of Technology, 344000 Fuzhou, Jiangxi, China;(2) Department of Mathematics, Hubei Institute for Nationalities, 445000 Enshi, Hubei Province, China;(3) Department of Biology and Agro-Industrial Economy, Via delle Scienze 208, 33100 Udine, Italy |
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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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