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Some New Properties of Wd-fuzzy Implication Algebras

Received: 23 April 2021     Accepted: 4 May 2021     Published: 27 May 2021
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Abstract

Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, Wd- FI-algebras, and other kinds of FI- algebras were reported. The main aim of this article is to study Wd-fuzzy implication algebras which are subalgebra of fuzzy implication algebras. We showed that Wd-fuzzy implication algebras are regular fuzzy implication algebras, but the inverse is not true. The relations between Wd-fuzzy implication algebras and other fuzzy algebras are discussed. Properties and axiomatic systems for Wd-fuzzy implication algebras are investigated. Furthermore, a few new results on Wd-fuzzy implication algebras has been added.

Published in Mathematics Letters (Volume 7, Issue 2)
DOI 10.11648/j.ml.20210702.12
Page(s) 25-29
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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), 2021. Published by Science Publishing Group

Keywords

Fuzzy Implication Algebras, Wd-Fuzzy Implication, Regular Fuzzy Implication Algebras, Heyting Type Fuzzy Implication Algebras

References
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[2] S. Massanet, G. Mayor, R. Mesiar, J. Torrens, On fuzzy implications: an axiomatic approach, International Journal of Approximate Reasoning, 2013, 54: 1471- 1482.
[3] Daowu Pei, A Survey of fuzzy implication algebras and their axiomatization. International Journal of Approximate Reasoning, 2014, 55: 1643-1658.
[4] Z. W. Li, G. H. Li, Some properties of fuzzy implication algebras, Fuzzy system and Mathematics. 2000, 14 (SI): 19-21 (in Chinese).
[5] Z. W. Li, G. H. Li, Structure properties of fuzzy implication algebras, J. Math. 2008, 28 (6): 701-705 (in Chinese).
[6] W. Chen, Some chararacters of regular fuzzy implication algebras, Fuzzy system and Mathematics. 2001, 15 (4): 24-27 (in Chinese).
[7] Z. W. Li, L. M. Sun, C. Y. Zheng, Regular fuzzy implication algebras, Fuzzy system and Mathematics. 2002, 16 (2): 22-26 (in Chinese).
[8] D. Wu, Commutative fuzzy implication algebras, Fuzzy system and Mathematics. 1999, 13 (1): 27-30 (in Chinese).
[9] F. A. Deng, J. L. Li, Wd− fuzzy implication algebras, J.Ha’erbin Norm. Univ. (Nat. Sci. Ed.) 1996, 12 (2): 18-21 (in Chinese).
[10] H. R. Zhang, L. C. Wang, Properties of LFI-algebras and residuated lattice, Fuzzy system and Mathematics. 2004, 18 (2): 13-17 (in Chinese).
[11] C. H. Liu, L. X. Xu, MP-filters of fuzzy implication algebras, Fuzzy system and Mathematics. 2009, 23 (2): 1-6 (in Chinese).
[12] C. H. Liu, L. X. Xu, Various concepts of fuzzy filters in FI-algebras, Fuzzy system and Mathematics. 2010, 24 (2): 21-27 (in Chinese).
[13] H. X. Wei, X. Q. Li, Rough set algebras and fuzzy implication algebras, Comput. Eng, APP., 2009, 45 (18): 38-39 (in Chinese).
[14] Y. Q. Zhu, A logic system based on FI-algebras and its completeness, Fuzzy system and Mathematics, 2005, 19 (2): 25-29 (in Chinese).
[15] Y. Zhu, Y. Xu, On filter theory of residuated lattices, Inf. Sci. 180 (19) (2010) 3614-3632.
[16] M. Kondo, W. A. Dudek, Filter theory of BL-algebras, Soft Comput. 12 (5) (2008) 419-423.
[17] M. Haveshki, E. Eslami, n-fold filters in BL-algebras, Math. Log. Q. 54 (2) (2008) 176-186.
[18] R. A. Borzooei, S. K. Shoar, R. Ameri, Some types of filters in MTL-algebras, Fuzzy Sets Syst. 187 (1) (2012) 92-102.
[19] M. Haveshki, A. Saeid, E. Eslami, Some types of filters in BL-algebras, SoftComput. 10 (8) (2006) 657-664.
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[21] Jianxiang Rong, Zuhua Liao, Yue Xi, Wei Song, Lun Li, Yong Li, On Derivations of FI-Algebras, International Conference on Fuzzy information and Engineering. ICFIE (2017) 68-80.
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    Fang-an Deng. (2021). Some New Properties of Wd-fuzzy Implication Algebras. Mathematics Letters, 7(2), 25-29. https://doi.org/10.11648/j.ml.20210702.12

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    ACS Style

    Fang-an Deng. Some New Properties of Wd-fuzzy Implication Algebras. Math. Lett. 2021, 7(2), 25-29. doi: 10.11648/j.ml.20210702.12

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    AMA Style

    Fang-an Deng. Some New Properties of Wd-fuzzy Implication Algebras. Math Lett. 2021;7(2):25-29. doi: 10.11648/j.ml.20210702.12

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  • @article{10.11648/j.ml.20210702.12,
      author = {Fang-an Deng},
      title = {Some New Properties of Wd-fuzzy Implication Algebras},
      journal = {Mathematics Letters},
      volume = {7},
      number = {2},
      pages = {25-29},
      doi = {10.11648/j.ml.20210702.12},
      url = {https://doi.org/10.11648/j.ml.20210702.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20210702.12},
      abstract = {Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, Wd- FI-algebras, and other kinds of FI- algebras were reported. The main aim of this article is to study Wd-fuzzy implication algebras which are subalgebra of fuzzy implication algebras. We showed that Wd-fuzzy implication algebras are regular fuzzy implication algebras, but the inverse is not true. The relations between Wd-fuzzy implication algebras and other fuzzy algebras are discussed. Properties and axiomatic systems for Wd-fuzzy implication algebras are investigated. Furthermore, a few new results on Wd-fuzzy implication algebras has been added.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Some New Properties of Wd-fuzzy Implication Algebras
    AU  - Fang-an Deng
    Y1  - 2021/05/27
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ml.20210702.12
    DO  - 10.11648/j.ml.20210702.12
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
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    EP  - 29
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20210702.12
    AB  - Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, Wd- FI-algebras, and other kinds of FI- algebras were reported. The main aim of this article is to study Wd-fuzzy implication algebras which are subalgebra of fuzzy implication algebras. We showed that Wd-fuzzy implication algebras are regular fuzzy implication algebras, but the inverse is not true. The relations between Wd-fuzzy implication algebras and other fuzzy algebras are discussed. Properties and axiomatic systems for Wd-fuzzy implication algebras are investigated. Furthermore, a few new results on Wd-fuzzy implication algebras has been added.
    VL  - 7
    IS  - 2
    ER  - 

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Author Information
  • School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong, P. R. China

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