Affiliations: [a]
School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu, People’s Republic of China | [b]
Department of Mathematics, Qinghai Normal University, Xining, People’s Republic of China | [c]
College of Information Engineering, Yancheng Teachers University, Jiangsu, People’s Republic of China
Correspondence:
[*]
Corresponding author. Zhudeng Wang, School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, People’s Republic of China. Tel.: +86 133 3798 7680; E-mail: zhudengwang2004@163.com.
Abstract: In this paper, we further investigate the constructions of implications and left (right) semi-uninorms on a complete lattice. We firstly give out the formulas for calculating the upper and lower approximation conjunctive left (right) semi-uninorms of a binary operation. Then, we derive the formulas for calculating the upper and lower approximation NP implications of a binary operation. Finally, we show that the right (left) residuum of the upper approximation conjunctive right (left) infinitely ∨-distributive left (right) semi-uninorm of a right (left) infinitely ∨-distributive binary operation is the lower approximation right infinitely ∧-distributive NP implication of the right (left) residuum of the binary operation.
