TY - JOUR
ID - 3046
TI - Implications, coimplications and left semi-uninorms on a complete lattice
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Wang, Yuan
AU - Tang, Keming
AU - Wang, Zhudeng
AD - College of Information Engineering, Yancheng Teachers University,
Jiangsu 224002, People's Republic of China
AD - School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, People's Republic of China
Y1 - 2017
PY - 2017
VL - 14
IS - 1
SP - 115
EP - 130
KW - Fuzzy connective
KW - Implication
KW - Coimplication
KW - Left semi-uninorm
KW - Neutrality principle
DO - 10.22111/ijfs.2017.3046
N2 - 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.
UR - http://ijfs.usb.ac.ir/article_3046.html
L1 - http://ijfs.usb.ac.ir/article_3046_01bd93593faf02d51d0a59def6a543fe.pdf
ER -