Applied and Computational Mathematics

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Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property

Received: 08 January 2017    Accepted: 19 January 2017    Published: 23 February 2017
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Abstract

We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left (right)-conjunctive left (right) arbitrary ˅-distributive left (right) semi-uninorms and lower approximation right arbitrary ˄-distributive implications which satisfy the order property.

DOI 10.11648/j.acm.20170601.13
Published in Applied and Computational Mathematics (Volume 6, Issue 1, February 2017)
Page(s) 45-53
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), 2024. Published by Science Publishing Group

Keywords

Fuzzy Logic, Fuzzy Connective, Left (Right) Semi-Uninorm, Implication, Strict Left (Right)-Conjunctive

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

  • 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

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  • APA Style

    Zhudeng Wang, Yuan Wang, Keming Tang. (2017). Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property. Applied and Computational Mathematics, 6(1), 45-53. https://doi.org/10.11648/j.acm.20170601.13

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    ACS Style

    Zhudeng Wang; Yuan Wang; Keming Tang. Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property. Appl. Comput. Math. 2017, 6(1), 45-53. doi: 10.11648/j.acm.20170601.13

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    AMA Style

    Zhudeng Wang, Yuan Wang, Keming Tang. Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property. Appl Comput Math. 2017;6(1):45-53. doi: 10.11648/j.acm.20170601.13

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  • @article{10.11648/j.acm.20170601.13,
      author = {Zhudeng Wang and Yuan Wang and Keming Tang},
      title = {Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property},
      journal = {Applied and Computational Mathematics},
      volume = {6},
      number = {1},
      pages = {45-53},
      doi = {10.11648/j.acm.20170601.13},
      url = {https://doi.org/10.11648/j.acm.20170601.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20170601.13},
      abstract = {We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left (right)-conjunctive left (right) arbitrary ˅-distributive left (right) semi-uninorms and lower approximation right arbitrary ˄-distributive implications which satisfy the order property.},
     year = {2017}
    }
    

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    T1  - Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property
    AU  - Zhudeng Wang
    AU  - Yuan Wang
    AU  - Keming Tang
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    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20170601.13
    AB  - We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left (right)-conjunctive left (right) arbitrary ˅-distributive left (right) semi-uninorms and lower approximation right arbitrary ˄-distributive implications which satisfy the order property.
    VL  - 6
    IS  - 1
    ER  - 

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