Affiliations: [a] School of Mathematical Sciences, Yancheng Teachers University, Jiangsu, People’s Republic of China | [b] Department of Mathematics, Qinghai Normal University, Xining, People’s Republic of China
Correspondence:
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Correspondence to: Zhudeng Wang, School of Mathematical Sciences, Yancheng Teachers University, Jiangsu 224002, People’s Republic of China. Tel.: +86 0515 88241216; [email protected]
Abstract: In this paper, we further study implications, coimplications and left (right) semi-uninorms on a complete lattice. We firstly show that the N-dual operation of the right (left) residual implication, which is generated by a left (right)-conjunctive right (left) infinitely ∨-distributive left (right) semi-uninorm, is the right (left) residual coimplication generated by its N-dual operation. As a dual result, the N-dual operation of the right (left) residual coimplication, which is generated by a left (right)-disjunctive right (left) infinitely ∧-distributive left (right) semi-uninorm, is the right (left) residual implication generated by its N-dual operation. Then, we demonstrate that the N-dual operations of the left (right) semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left (right) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) infinitely ∨-distributive left (right) semi-uninorms induced by implications and disjunctive right (left) infinitely ∧-distributive left (right) semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.
Keywords: Fuzzy connective, implication, coimplication, left (right) semi-uninorm, neutrality principle
