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 |
| 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. |
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Copyright © The Author(s), 2021. Published by Science Publishing Group |
Fuzzy Implication Algebras, Wd-Fuzzy Implication, Regular Fuzzy Implication Algebras, Heyting Type Fuzzy Implication Algebras
| [1] | Wu Wangming, Fuzzy implication algebra, Fuzzy systems and Mathematics, No. 1 (1990): 56-64. |
| [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. |
| [20] | Ivan Chajda, Jan Paseka, Tense operators in fuzzy logic, Fuzzy Sets Syst. 276 (1) (2015) 100-113. |
| [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. |
| [22] | Diego N. Castano, Implicative subreducts of MV- algebras: free and weakly projective objects, Algebra universalis. 78 (2017) 579-600. |
| [23] | Sergio Arturo Celani, Complete and atomic Tarski algebras, Archive for Mathematical Logic. 58 (2019): 899-914. |
| [24] | Songsong Dai, A note on implication operators of quantum logic, Quantum Machine Intelligence (2020) 2-15. |
APA Style
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
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
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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Download@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}
}
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 SP - 25 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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