TY - JOUR
ID - 6560
TI - Construction of 2-uninorms on bounded lattices
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Xie, A.
AU - Yi, Z.
AD - Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi, 330031, China
AD - College of Mathematics and Information Science, Nanchang Normal University, Nanchang, Jiangxi, 330031, China
Y1 - 2022
PY - 2022
VL - 19
IS - 1
SP - 189
EP - 200
DO - 10.22111/ijfs.2022.6560
N2 - Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U_1 and U_2, defined on sublattices [0,d] and [d,1], respectively, this paper presents two methods for constructing binary operators on L which extend both U_1 and U_2. We show that our first construction is a 2-uninorm on L if and only if U_2 is conjunctive and our second construction is a 2-uninorm on L if and only if U_1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0,d]^2 and [d,1]^2 are respectively U_1 and U_2.
UR - https://ijfs.usb.ac.ir/article_6560.html
L1 - https://ijfs.usb.ac.ir/article_6560_9220983cc8033753db150b6234633b42.pdf
ER -