New structures for uninorms on bounded lattices¹

Article type: Research Article

Authors: Xiu, Zhen-Yu | Jiang, Yu-Xiu^{; *}

Affiliations: College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P.R. China

Correspondence: [*] Corresponding author. Yu-Xiu Jiang, College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, P.R. China. E-mail: 191158845@qq.com.

Note: [1] The project is supported by the National Natural Science Foundation of China (No. 11871097, 12271036).

Abstract: In this article, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are sufficient and necessary for the uninorms. Moreover, some illustrative examples for the construction of uninorms are provided. At last, we show that the additional constraints on t-norms (t-conorms) and t-subnorms (t-subconorms) of some uninorms in the literature are exactly sufficient and necessary.

Keywords: Bounded lattices, t-norms, t-subnorms, uninorms

DOI: 10.3233/JIFS-224537

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 2, pp. 2019-2030, 2023