Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice
Automation, Control and Intelligent Systems
Volume 2, Issue 3, June 2014, Pages: 33-41
Received: Aug. 4, 2014; Accepted: Aug. 18, 2014; Published: Aug. 30, 2014
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Authors
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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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.
Keywords
Fuzzy Logic, Fuzzy Connective, Left (Right) Semi-Uninorm, Implication, Neutrality Principle, Order Property
To cite this article
Yuan Wang, Keming Tang, Zhudeng Wang, Some Relationships between Left (Right) Semi-Uninorms and Implications on a Complete Lattice, Automation, Control and Intelligent Systems. Vol. 2, No. 3, 2014, pp. 33-41. doi: 10.11648/j.acis.20140203.12
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