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L-information systems and complete L-lattices

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Abstract

In this paper, the relationship between complete L-lattices and L-closure systems is investigated first. That is, each L-closure system is a complete L-lattice under the fuzzy inclusion order, and each complete L-lattice is isomorphic to an L-closure system. Next, we focus on information systems in fuzzy setting and propose the concept of L-information systems from the viewpoint of fuzzy logic. The cheerful result that L-information systems are a representation of complete L-lattices is presented. Furthermore, we define appropriate morphisms on L-information systems and complete L-lattices, respectively, and prove that they are categorically equivalent.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (NO. 11071061), the National Basic Research Program (NO. 2011CB311808) and Hunan Provincial Innovation Foundation for Postgraduate (NO. CX2011B158).

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Hongping Liu, Qingguo Li & Xiangnan Zhou

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  1. Hongping Liu
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  2. Qingguo Li
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  3. Xiangnan Zhou
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Correspondence to Qingguo Li.

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Liu, H., Li, Q. & Zhou, X. L-information systems and complete L-lattices. Neural Comput & Applic 23, 1139–1147 (2013). https://doi.org/10.1007/s00521-012-1060-9

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