%0 Journal Article
%T Construction of 2-uninorms on bounded lattices
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Xie, A.
%A Yi, Z.
%D 2022
%\ 02/01/2022
%V 19
%N 1
%P 189-200
%! Construction of 2-uninorms on bounded lattices
%R 10.22111/ijfs.2022.6560
%X 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.
%U https://ijfs.usb.ac.ir/article_6560_9220983cc8033753db150b6234633b42.pdf