%0 Journal Article
%T Implications, coimplications and left semi-uninorms on a complete lattice
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Wang, Yuan
%A Tang, Keming
%A Wang, Zhudeng
%D 2017
%\ 02/28/2017
%V 14
%N 1
%P 115-130
%! Implications, coimplications and left semi-uninorms on a complete lattice
%K Fuzzy connective
%K Implication
%K Coimplication
%K Left semi-uninorm
%K Neutrality principle
%R 10.22111/ijfs.2017.3046
%X In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $\vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $\wedge$-distributive left semi-uninorm, is the right residual implication induced by its $N$-dual operation. Then, we demonstrate that the $N$-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. Finally, we reveal the relationships between conjunctive right arbitrary $\vee$-distributive left semi-uninorms induced by implications and disjunctive right arbitrary $\wedge$-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.
%U https://ijfs.usb.ac.ir/article_3046_01bd93593faf02d51d0a59def6a543fe.pdf