Constructing conjunctive left (right) semi-uninorms and implications satisfying the neutrality principle
Xiaoying Hao, Meixia Niu, Yuan Wang, Zhudeng Wang · Journal of Intelligent & Fuzzy Systems · 2016
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.