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Constructions of Implications Satisfying the Order Property on a Complete Lattice

Received: 7 January 2017     Accepted: 19 January 2017     Published: 23 February 2017
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Abstract

In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.

Published in Automation, Control and Intelligent Systems (Volume 5, Issue 1)
DOI 10.11648/j.acis.20170501.11
Page(s) 1-7
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), 2017. Published by Science Publishing Group

Keywords

Fuzzy Logic, Fuzzy Connective, Implication, Order Property

References
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  • APA Style

    Yuan Wang, Keming Tang, Zhudeng Wang. (2017). Constructions of Implications Satisfying the Order Property on a Complete Lattice. Automation, Control and Intelligent Systems, 5(1), 1-7. https://doi.org/10.11648/j.acis.20170501.11

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    ACS Style

    Yuan Wang; Keming Tang; Zhudeng Wang. Constructions of Implications Satisfying the Order Property on a Complete Lattice. Autom. Control Intell. Syst. 2017, 5(1), 1-7. doi: 10.11648/j.acis.20170501.11

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    AMA Style

    Yuan Wang, Keming Tang, Zhudeng Wang. Constructions of Implications Satisfying the Order Property on a Complete Lattice. Autom Control Intell Syst. 2017;5(1):1-7. doi: 10.11648/j.acis.20170501.11

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  • @article{10.11648/j.acis.20170501.11,
      author = {Yuan Wang and Keming Tang and Zhudeng Wang},
      title = {Constructions of Implications Satisfying the Order Property on a Complete Lattice},
      journal = {Automation, Control and Intelligent Systems},
      volume = {5},
      number = {1},
      pages = {1-7},
      doi = {10.11648/j.acis.20170501.11},
      url = {https://doi.org/10.11648/j.acis.20170501.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20170501.11},
      abstract = {In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.},
     year = {2017}
    }
    

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    T1  - Constructions of Implications Satisfying the Order Property on a Complete Lattice
    AU  - Yuan Wang
    AU  - Keming Tang
    AU  - Zhudeng Wang
    Y1  - 2017/02/23
    PY  - 2017
    N1  - https://doi.org/10.11648/j.acis.20170501.11
    DO  - 10.11648/j.acis.20170501.11
    T2  - Automation, Control and Intelligent Systems
    JF  - Automation, Control and Intelligent Systems
    JO  - Automation, Control and Intelligent Systems
    SP  - 1
    EP  - 7
    PB  - Science Publishing Group
    SN  - 2328-5591
    UR  - https://doi.org/10.11648/j.acis.20170501.11
    AB  - In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.
    VL  - 5
    IS  - 1
    ER  - 

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Author Information
  • College of Information Science and Technology, Yancheng Teachers University, Yancheng, People's Republic of China

  • College of Information Science and Technology, Yancheng Teachers University, Yancheng, People's Republic of China

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

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