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A Note on L-fuzzy Closure Systems

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Abstract

In this paper, a new notion of (v-consistent) L *-closure L-system is proposed where L is a complete residuated lattice and \(*\) is a truth stresser on L. The one-to-one correspondence between (v-consistent) L *-closure L-systems and (v-consistent) L *-closure operators is established. Furthermore, the notion of v-consistent L *-closure system is introduced. It is shown that the notion of (v-consistent) L *-closure L-system provides an alternative way to characterize (v-consistent) L *-closure systems. Finally, the category of (v-consistent) L *-closure system spaces is introduced in virtue of the notion of continuous mapping. It is shown that the categories of L *-closure L-system spaces, L *-closure spaces and L *-closure system spaces are isomorphic with each other.

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Acknowledgments

We would like to thank the anonymous referees for their professional comments and valuable suggestions. This work is supported by the National Natural Science Foundation of China (No. 11401195, 11371130), Research Fund for the Doctoral Program of Higher Education of China (No. 20120161110017), Hunan Provincial Natural Science Foundation of China (No. 2015JJ3050). It is also partly supported by the Scientic Research Foundation for Returned Scholars, Ministry of Education of China, of the first author.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410006, People’s Republic of China

    Lankun Guo

  2. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, People’s Republic of China

    Qingguo Li

  3. Institute of Biomedical Informatics, University of Kentucky, Lexington, KY, 40536, USA

    Guo-Qiang Zhang

Authors
  1. Lankun Guo
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  2. Qingguo Li
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  3. Guo-Qiang Zhang
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Correspondence to Qingguo Li.

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Guo, L., Li, Q. & Zhang, GQ. A Note on L-fuzzy Closure Systems. Int. J. Fuzzy Syst. 18, 110–118 (2016). https://doi.org/10.1007/s40815-015-0104-6

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  • DOI: https://doi.org/10.1007/s40815-015-0104-6

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