Collective relations of fuzzy relational structures

Article type: Research Article

Authors: Du, Yi-Bin^{a; b; *} | Zhu, Ping^c

Affiliations: [a] Automation School, Beijing University of Posts and Telecommunications, Beijing, P.R. China | [b] University of Foreign Languages, Luoyang, Henan, P.R. China | [c] School of Science, Beijing University of Posts and Telecommunications, Beijing, P.R. China

Correspondence: [*] Corresponding author. Yi-Bin Du. E-mail: duyibin@bupt.edu.cn.

Abstract: This paper focuses on fuzzy relational structures. In order to collect the knowledge that has been acquired with regard to fuzzy relational structures, the concept of collective relations is proposed and characterizations of collective relations are investigated. A method on computing the largest collective relation is further given. Moreover, based on substructures of fuzzy relational structures, a decomposition theorem of collective relations is obtained and weak collective relations and strong collective relations are put forward. Finally, the fuzzy rough set analysis of fuzzy relational structures is discussed.

Keywords: Residuated lattice, fuzzy set, fuzzy relational structure, collective relation, fuzzy rough set

DOI: 10.3233/JIFS-17969

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2807-2816, 2018