| Peer-Reviewed

Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms on a Complete Lattice

Received: 6 January 2017    Accepted: 19 January 2017    Published: 23 February 2017
Views:       Downloads:
Abstract

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

Published in International Journal of Intelligent Information Systems (Volume 6, Issue 1)
DOI 10.11648/j.ijiis.20170601.11
Page(s) 1-6
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, Strict Left (Right)-Conjunctive

References
[1] R. R. Yager and A. Rybalov, “Uninorm aggregation operators”, Fuzzy Sets and Systems, 80, 111-120, 1996.
[2] J. Fodor, R. R. Yager and A. Rybalov, “Structure of uninorms”, Internat. J. Uncertainly, Fuzziness and Knowledge-Based Systems, 5, 411-427, 1997.
[3] D. Gabbay and G. Metcalfe, “fuzzy logics based on [0,1)-continuous uninorms”, Arch. Math. Logic, 46, 425-449, 2007.
[4] A. K. Tsadiras and K. G. Margaritis, “The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons”, Fuzzy Sets and Systems, 93, 263-274, 1998.
[5] R. R. Yager, “Uninorms in fuzzy system modeling”, Fuzzy Sets and Systems, 122, 167-175, 2001.
[6] R. R. Yager, “Defending against strategic manipulation in uninorm-based multi-agent decision making”, European J. Oper. Res., 141, 217-232, 2002.
[7] M. Mas, M. Monserrat and J. Torrens, “On left and right uninorms”, Internat. J. Uncertainly, Fuzziness and Knowledge-Based Systems, 9, 491-507, 2001.
[8] M. Mas, M. Monserrat, and J. Torrens, “On left and right uninorms on a finite chain”, Fuzzy Sets and Systems, 146, 3-17, 2004.
[9] Z. D. Wang and J. X. Fang, “Residual operators of left and right uninorms on a complete lattice”, Fuzzy Sets and Systems, 160, 22-31, 2009.
[10] Z. D. Wang and J. X. Fang, “Residual coimplicators of left and right uninorms on a complete lattice”, Fuzzy Sets and Systems, 160, 2086-2096, 2009.
[11] H. W. Liu, “Semi-uninorm and implications on a complete lattice”, Fuzzy Sets and Systems, 191, 72-82, 2012.
[12] Y. Su, Z. D. Wang and K. M. Tang, “Left and right semi-uninorms on a complete lattice”, Kybernetika, 49, 948-961, 2013.
[13] B. De Baets and J. Fodor, “Residual operators of uninorms”, Soft Computing, 3, 89-100, 1999.
[14] M. Mas, M. Monserrat and J. Torrens, “Two types of implications derived from uninorms”, Fuzzy Sets and Systems, 158, 2612-2626, 2007.
[15] S. Jenei and F. Montagna, “A general method for constructing left-continuous t-norms”, Fuzzy Sets and Systems, 136, 263-282, 2003.
[16] Z. D. Wang, “Generating pseudo-t-norms and implication operators”, Fuzzy Sets and Systems, 157, 398-410, 2006.
[17] Y. Su and Z. D. Wang, “Constructing implications and coimplications on a complete lattice”, Fuzzy Sets and Systems, 247, 68-80, 2014.
[18] X. Y. Hao, M. X. Niu and Z. D. Wang, “The relations between implications and left (right) semi-uninorms on a complete lattice”, Internat. J. Uncertainly, Fuzziness and Knowledge-Based Systems, 23, 245-261, 2015.
[19] X. Y. Hao, M. X. Niu, Y. Wang and Z. D. Wang, “Constructing conjunctive left (right) semi-uninorms and implications satisfying the neutrality principle”, Journal of Intelligent and Fuzzy Systems, 31, 1819-1829, 2016.
[20] Z. D. Wang, “Left (right) semi-uninorms and coimplications on a complete lattice”, Fuzzy Sets and Systems, 287, 227-239, 2016.
[21] X. Y. Hao, M. X. Niu, Y. Wang and Z. D. Wang, “Constructing conjunctive left (right) semi-uninorms and implications satisfying the neutrality principle”, Journal of Intelligent and Fuzzy Systems, 31, 1819-1829, 2016.
[22] Z. D. Wang, M. X. Niu and X. Y. Hao, “Constructions of coimplications and left (right) semi-uninorms on a complete lattice”, Information Sciences, 317, 181-195, 2015.
[23] G. Birkhoff, “Lattice Theory”, American Mathematical Society Colloquium Publishers, Providence, 1967.
Cite This Article
  • APA Style

    Yuan Wang, Keming Tang, Zhudeng Wang. (2017). Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms on a Complete Lattice. International Journal of Intelligent Information Systems, 6(1), 1-6. https://doi.org/10.11648/j.ijiis.20170601.11

    Copy | Download

    ACS Style

    Yuan Wang; Keming Tang; Zhudeng Wang. Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms on a Complete Lattice. Int. J. Intell. Inf. Syst. 2017, 6(1), 1-6. doi: 10.11648/j.ijiis.20170601.11

    Copy | Download

    AMA Style

    Yuan Wang, Keming Tang, Zhudeng Wang. Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms on a Complete Lattice. Int J Intell Inf Syst. 2017;6(1):1-6. doi: 10.11648/j.ijiis.20170601.11

    Copy | Download

  • @article{10.11648/j.ijiis.20170601.11,
      author = {Yuan Wang and Keming Tang and Zhudeng Wang},
      title = {Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms on a Complete Lattice},
      journal = {International Journal of Intelligent Information Systems},
      volume = {6},
      number = {1},
      pages = {1-6},
      doi = {10.11648/j.ijiis.20170601.11},
      url = {https://doi.org/10.11648/j.ijiis.20170601.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijiis.20170601.11},
      abstract = {In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of strict left (right)-conjunctive left (right) semi-uninorms by means of some examples. Then we give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation.},
     year = {2017}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms 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.ijiis.20170601.11
    DO  - 10.11648/j.ijiis.20170601.11
    T2  - International Journal of Intelligent Information Systems
    JF  - International Journal of Intelligent Information Systems
    JO  - International Journal of Intelligent Information Systems
    SP  - 1
    EP  - 6
    PB  - Science Publishing Group
    SN  - 2328-7683
    UR  - https://doi.org/10.11648/j.ijiis.20170601.11
    AB  - In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of strict left (right)-conjunctive left (right) semi-uninorms by means of some examples. Then we give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation.
    VL  - 6
    IS  - 1
    ER  - 

    Copy | Download

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, Yancheng, People's Republic of China

  • Sections