Document Type : Research Paper

**Authors**

^{1}
Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi, 330031, China

^{2}
College of Mathematics and Information Science, Nanchang Normal University, Nanchang, Jiangxi, 330031, China

**Abstract**

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.

**Keywords**

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January and February 2022

Pages 189-200