Further study of multi-granulation fuzzy rough sets

Article type: Research Article

Authors: Kong, Qingzhao^{a; b; *} | Wei, Zengxin^c

Affiliations: [a] School of Science, East China University of Science and Technology, Shanghai, P.R. China | [b] School of Science, Jimei University, Xiamen, P.R. China | [c] School of Mathematics and Information, Guangxi University, Nanning, P.R. China

Correspondence: [*] Corresponding author. Qingzhao Kong, School of Science, Jimei University, Xiamen 361021, P.R. China. Tel.: +86 0592 13860112994; Fax: +86 0592 6181044; E-mail: kongqingzhao@163.com..

Abstract: The multi-granulation fuzzy rough sets (MGFRS), proposed by Xu [35], is a meaningful contribution in the view of the generalization of the classical rough set model. In this paper, the main objective is to make further studies based on reference [35]. It is shown that the MGFRS do not meet the operations of intersection and union. To solve these problems, we propose the concepts of the equivalence relations with minimum (maximum) element and find that the MGFRS based on the equivalence relations with minimum (maximum) element meet the operations of intersection and union. At the same time, some algebraic properties of the MGFRS are discussed.

Keywords: Fuzzy rough set, multiple granulation, minimum (maximum) element, operation property, algebraic property

DOI: 10.3233/JIFS-16373

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2413-2424, 2017