Multi-granulation rough filters and rough fuzzy filters in Pseudo-BCI algebras

Article type: Research Article

Authors: Shao, Songtao^a | Zhang, Xiaohong^{a; b; *} | Bo, Chunxin^a | Park, Choonkil^c

Affiliations: [a] College of Information Engineering, Shanghai Maritime University, Shanghai, P.R. China | [b] Department of Mathematics, School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an, P.R. China | [c] Department of Mathematics, Hanyang University, Seoul, South Korea

Correspondence: [*] Corresponding author. Xiaohong Zhang. E-mails: zhangxh@shmtu.edu.cn and zhangxiaohong@sust.edu.cn.

Abstract: This paper introduced the notions of rough filters, multi-granulation rough filters, and rough fuzzy filters in pseudo-BCI algebras and investigated some properties. First, a congruence relation was structured by a filter on pseudo-BCI algebra. Then rough filters and rough fuzzy filters were investigated. Next, the relationships between upper (lower) rough filters and upper (lower) approximations of their fuzzy homomorphic images were discussed. Furthermore, original rough filter model was extended to a multi-granulation rough filter model, where the set approximations were defined by using multi congruence relations on pseudo-BCI algebra.

Keywords: Pseudo-BCI algebra, rough set, fuzzy set, multi-granulation rough set

DOI: 10.3233/JIFS-18144

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 6, pp. 4377-4386, 2018