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

Zhudeng Wang; Yuan Wang; Keming Tang

doi:doi:10.11648/j.acm.20170601.13

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

Zhudeng Wang, Yuan Wang, Keming Tang

Published in Applied and Computational Mathematics (Volume 6, Issue 1)

Received: 8 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.

Published in	Applied and Computational Mathematics (Volume 6, Issue 1)
DOI	10.11648/j.acm.20170601.13
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), 2017. Published by Science Publishing Group

Keywords

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

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property
AU  - Zhudeng Wang
AU  - Yuan Wang
AU  - Keming Tang
Y1  - 2017/02/23
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170601.13
DO  - 10.11648/j.acm.20170601.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 45
EP  - 53
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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Author Information

Zhudeng Wang

School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, People's Republic of China
Yuan Wang

College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China
Keming Tang

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property
AU  - Zhudeng Wang
AU  - Yuan Wang
AU  - Keming Tang
Y1  - 2017/02/23
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170601.13
DO  - 10.11648/j.acm.20170601.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 45
EP  - 53
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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