Structures of fuzzy truth values based on a type-2 fuzzy set

Article type: Research Article

Authors: Qin, Bin^{; *}

Affiliations: School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R. China

Correspondence: [*] Corresponding author. Bin Qin, School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P.R. China E-mail:402503@gxun.edu.cn.

Abstract: In this paper, based on a type-2 fuzzy set, structures of fuzzy truth values on a linearly ordered set are investigated. Some special type-2 fuzzy sets are first presented. Then, rough approximations of fuzzy truth values based on a type-2 fuzzy set are introduced. Next, topological and rough structures of fuzzy truth values based on a type-2 fuzzy set are obtained. Finally, rough equal relations of fuzzy truth values based on a type-2 fuzzy set are proposed. These results will be helpful for the study of type-2 fuzzy sets.

Keywords: Type-2 fuzzy sets, fuzzy truth values, structures, fuzzy topologies, rough approximations, rough equal relations

DOI: 10.3233/JIFS-18082

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 3, pp. 3553-3566, 2018