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Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”

Received: 29 February 2016     Accepted: 9 March 2016     Published: 23 March 2016
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Abstract

In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.

Published in Automation, Control and Intelligent Systems (Volume 4, Issue 2)
DOI 10.11648/j.acis.20160402.11
Page(s) 10-14
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Involutive Residuated Lattice, L-relation, L-fuzzy Topology, L-fuzzy Approximation Space

References
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[4] Y. Liu and Y. Lin, “Intuitionistic fuzzy rough set model based on conflict distance and applications”, Applied Soft Computing, 31, 266-273, 2015.
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[9] A. M. Radzikowska and E. E. Kerre, “Fuzzy rough sets based onresiduated lattices”, in: J. F. Peter et al. (Eds.), Transactions on Rough Sets II, LNCS 3135, 278-296, 2004.
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  • APA Style

    Yuan Wang, Keming Tang, Zhudeng Wang. (2016). Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Automation, Control and Intelligent Systems, 4(2), 10-14. https://doi.org/10.11648/j.acis.20160402.11

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    ACS Style

    Yuan Wang; Keming Tang; Zhudeng Wang. Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Autom. Control Intell. Syst. 2016, 4(2), 10-14. doi: 10.11648/j.acis.20160402.11

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    AMA Style

    Yuan Wang, Keming Tang, Zhudeng Wang. Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Autom Control Intell Syst. 2016;4(2):10-14. doi: 10.11648/j.acis.20160402.11

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  • @article{10.11648/j.acis.20160402.11,
      author = {Yuan Wang and Keming Tang and Zhudeng Wang},
      title = {Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”},
      journal = {Automation, Control and Intelligent Systems},
      volume = {4},
      number = {2},
      pages = {10-14},
      doi = {10.11648/j.acis.20160402.11},
      url = {https://doi.org/10.11648/j.acis.20160402.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20160402.11},
      abstract = {In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”
    AU  - Yuan Wang
    AU  - Keming Tang
    AU  - Zhudeng Wang
    Y1  - 2016/03/23
    PY  - 2016
    N1  - https://doi.org/10.11648/j.acis.20160402.11
    DO  - 10.11648/j.acis.20160402.11
    T2  - Automation, Control and Intelligent Systems
    JF  - Automation, Control and Intelligent Systems
    JO  - Automation, Control and Intelligent Systems
    SP  - 10
    EP  - 14
    PB  - Science Publishing Group
    SN  - 2328-5591
    UR  - https://doi.org/10.11648/j.acis.20160402.11
    AB  - In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.
    VL  - 4
    IS  - 2
    ER  - 

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Author Information
  • College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China

  • College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China

  • School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu, People's Republic of China

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