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), 2024. Published by Science Publishing Group |
Fuzzy Implication Algebras, Wd-Fuzzy Implication, Regular Fuzzy Implication Algebras, Heyting Type Fuzzy Implication Algebras
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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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