Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice

Yuan Wang; Keming Tang; Zhudeng Wang

doi:doi:10.11648/j.acis.20140203.12

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Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice

Yuan Wang, Keming Tang, Zhudeng Wang

Published in Automation, Control and Intelligent Systems (Volume 2, Issue 3)

Received: 4 August 2014 Accepted: 18 August 2014 Published: 30 August 2014

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Abstract

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, we investigate the left and right semi-uninorms induced by an implication, give some conditions such that two operations induced by an implication constitute left or right semi-uninorms, and demonstrate that the operations induced by a right ∧-distributive implication, which satisfies the order property or neutrality principle, are left (right) ∨-distributive left (right) semi-uninorms or right (left) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) ∨-distributive left (right) semi-uninorms and right ∧-distributive implications which satisfy the neutrality principle.

Published in	Automation, Control and Intelligent Systems (Volume 2, Issue 3)
DOI	10.11648/j.acis.20140203.12
Page(s)	33-41
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, Left (Right) Semi-Uninorm, Implication, Neutrality Principle, Order Property

References

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APA Style

Yuan Wang, Keming Tang, Zhudeng Wang. (2014). Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice. Automation, Control and Intelligent Systems, 2(3), 33-41. https://doi.org/10.11648/j.acis.20140203.12

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ACS Style

Yuan Wang; Keming Tang; Zhudeng Wang. Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice. Autom. Control Intell. Syst. 2014, 2(3), 33-41. doi: 10.11648/j.acis.20140203.12

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AMA Style

Yuan Wang, Keming Tang, Zhudeng Wang. Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice. Autom Control Intell Syst. 2014;2(3):33-41. doi: 10.11648/j.acis.20140203.12

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@article{10.11648/j.acis.20140203.12,
  author = {Yuan Wang and Keming Tang and Zhudeng Wang},
  title = {Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice},
  journal = {Automation, Control and Intelligent Systems},
  volume = {2},
  number = {3},
  pages = {33-41},
  doi = {10.11648/j.acis.20140203.12},
  url = {https://doi.org/10.11648/j.acis.20140203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20140203.12},
  abstract = {In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, we investigate the left and right semi-uninorms induced by an implication, give some conditions such that two operations induced by an implication constitute left or right semi-uninorms, and demonstrate that the operations induced by a right ∧-distributive implication, which satisfies the order property or neutrality principle, are left (right) ∨-distributive left (right) semi-uninorms or right (left) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) ∨-distributive left (right) semi-uninorms and right ∧-distributive implications which satisfy the neutrality principle.},
 year = {2014}
}

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TY  - JOUR
T1  - Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice
AU  - Yuan Wang
AU  - Keming Tang
AU  - Zhudeng Wang
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acis.20140203.12
DO  - 10.11648/j.acis.20140203.12
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 33
EP  - 41
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20140203.12
AB  - In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, we investigate the left and right semi-uninorms induced by an implication, give some conditions such that two operations induced by an implication constitute left or right semi-uninorms, and demonstrate that the operations induced by a right ∧-distributive implication, which satisfies the order property or neutrality principle, are left (right) ∨-distributive left (right) semi-uninorms or right (left) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) ∨-distributive left (right) semi-uninorms and right ∧-distributive implications which satisfy the neutrality principle.
VL  - 2
IS  - 3
ER  -

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Author Information

Yuan Wang

College of Information Science and Technology, Yancheng Teachers University, Yancheng 224002, People's Republic of China
Keming Tang

College of Information Science and Technology, Yancheng Teachers University, Yancheng 224002, People's Republic of China
Zhudeng Wang

School of Mathematical Sciences, Yancheng Teachers University, Jiangsu 224002, People's Republic of China

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Plain Text BibTeX RIS

APA Style

Yuan Wang, Keming Tang, Zhudeng Wang. (2014). Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice. Automation, Control and Intelligent Systems, 2(3), 33-41. https://doi.org/10.11648/j.acis.20140203.12

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ACS Style

Yuan Wang; Keming Tang; Zhudeng Wang. Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice. Autom. Control Intell. Syst. 2014, 2(3), 33-41. doi: 10.11648/j.acis.20140203.12

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AMA Style

Yuan Wang, Keming Tang, Zhudeng Wang. Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice. Autom Control Intell Syst. 2014;2(3):33-41. doi: 10.11648/j.acis.20140203.12

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@article{10.11648/j.acis.20140203.12,
  author = {Yuan Wang and Keming Tang and Zhudeng Wang},
  title = {Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice},
  journal = {Automation, Control and Intelligent Systems},
  volume = {2},
  number = {3},
  pages = {33-41},
  doi = {10.11648/j.acis.20140203.12},
  url = {https://doi.org/10.11648/j.acis.20140203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20140203.12},
  abstract = {In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, we investigate the left and right semi-uninorms induced by an implication, give some conditions such that two operations induced by an implication constitute left or right semi-uninorms, and demonstrate that the operations induced by a right ∧-distributive implication, which satisfies the order property or neutrality principle, are left (right) ∨-distributive left (right) semi-uninorms or right (left) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) ∨-distributive left (right) semi-uninorms and right ∧-distributive implications which satisfy the neutrality principle.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice
AU  - Yuan Wang
AU  - Keming Tang
AU  - Zhudeng Wang
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acis.20140203.12
DO  - 10.11648/j.acis.20140203.12
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 33
EP  - 41
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20140203.12
AB  - In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, we investigate the left and right semi-uninorms induced by an implication, give some conditions such that two operations induced by an implication constitute left or right semi-uninorms, and demonstrate that the operations induced by a right ∧-distributive implication, which satisfies the order property or neutrality principle, are left (right) ∨-distributive left (right) semi-uninorms or right (left) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) ∨-distributive left (right) semi-uninorms and right ∧-distributive implications which satisfy the neutrality principle.
VL  - 2
IS  - 3
ER  -

Copy | Download