Constructions of Implications Satisfying the Order Property on a Complete Lattice

Yuan Wang; Keming Tang; Zhudeng Wang

doi:doi:10.11648/j.acis.20170501.11

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Constructions of Implications Satisfying the Order Property on a Complete Lattice

Yuan Wang, Keming Tang, Zhudeng Wang

Published in Automation, Control and Intelligent Systems (Volume 5, Issue 1)

Received: 7 January 2017 Accepted: 19 January 2017 Published: 23 February 2017

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Abstract

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

Published in	Automation, Control and Intelligent Systems (Volume 5, Issue 1)
DOI	10.11648/j.acis.20170501.11
Page(s)	1-7
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, Implication, Order Property

References

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APA Style

Yuan Wang, Keming Tang, Zhudeng Wang. (2017). Constructions of Implications Satisfying the Order Property on a Complete Lattice. Automation, Control and Intelligent Systems, 5(1), 1-7. https://doi.org/10.11648/j.acis.20170501.11

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ACS Style

Yuan Wang; Keming Tang; Zhudeng Wang. Constructions of Implications Satisfying the Order Property on a Complete Lattice. Autom. Control Intell. Syst. 2017, 5(1), 1-7. doi: 10.11648/j.acis.20170501.11

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AMA Style

Yuan Wang, Keming Tang, Zhudeng Wang. Constructions of Implications Satisfying the Order Property on a Complete Lattice. Autom Control Intell Syst. 2017;5(1):1-7. doi: 10.11648/j.acis.20170501.11

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@article{10.11648/j.acis.20170501.11,
  author = {Yuan Wang and Keming Tang and Zhudeng Wang},
  title = {Constructions of Implications Satisfying the Order Property on a Complete Lattice},
  journal = {Automation, Control and Intelligent Systems},
  volume = {5},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.acis.20170501.11},
  url = {https://doi.org/10.11648/j.acis.20170501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20170501.11},
  abstract = {In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.},
 year = {2017}
}

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TY  - JOUR
T1  - Constructions of Implications Satisfying the Order Property 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.acis.20170501.11
DO  - 10.11648/j.acis.20170501.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2328-5591
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AB  - In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.
VL  - 5
IS  - 1
ER  -

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Author Information

Yuan Wang

College of Information Science and Technology, Yancheng Teachers University, Yancheng, People's Republic of China
Keming Tang

College of Information Science and Technology, Yancheng Teachers University, Yancheng, People's Republic of China
Zhudeng Wang

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

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APA Style

Yuan Wang, Keming Tang, Zhudeng Wang. (2017). Constructions of Implications Satisfying the Order Property on a Complete Lattice. Automation, Control and Intelligent Systems, 5(1), 1-7. https://doi.org/10.11648/j.acis.20170501.11

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ACS Style

Yuan Wang; Keming Tang; Zhudeng Wang. Constructions of Implications Satisfying the Order Property on a Complete Lattice. Autom. Control Intell. Syst. 2017, 5(1), 1-7. doi: 10.11648/j.acis.20170501.11

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AMA Style

Yuan Wang, Keming Tang, Zhudeng Wang. Constructions of Implications Satisfying the Order Property on a Complete Lattice. Autom Control Intell Syst. 2017;5(1):1-7. doi: 10.11648/j.acis.20170501.11

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@article{10.11648/j.acis.20170501.11,
  author = {Yuan Wang and Keming Tang and Zhudeng Wang},
  title = {Constructions of Implications Satisfying the Order Property on a Complete Lattice},
  journal = {Automation, Control and Intelligent Systems},
  volume = {5},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.acis.20170501.11},
  url = {https://doi.org/10.11648/j.acis.20170501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20170501.11},
  abstract = {In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Constructions of Implications Satisfying the Order Property 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.acis.20170501.11
DO  - 10.11648/j.acis.20170501.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20170501.11
AB  - In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.
VL  - 5
IS  - 1
ER  -

Copy | Download