Roughness in m-semilattices¹

Article type: Research Article

Authors: Zhou, Xin^{a; b; *} | Zhao, Bin^a | Han, Shengwei^a

Affiliations: [a] College of Mathematics and Information Science, Shaanxi NormalUniversity, Xi’an, P.R. China | [b] School of Science, Xi’an Polytechnic University, Xi’an, P.R. China

Correspondence: [*] Corresponding author. Xin Zhou, E-mail: sxxzx1986@163.com.

Note: [] The research is supported by the National Natural Science Foundation of China (Grant nos. 11501435, 11301316), the Natural Science Program for Basic Research of Shaanxi Province (Grant no. 2015JM1020) and the Fundamental Research Funds for the Central Universities (Grant no. GK201302003).

Abstract: In this paper, we consider roughness in m-semilattices, which combine the ∨-semilattice structure and the operation · of a semigroup. Firstly, we propose some kinds of equivalence relations on m-semilattices and investigate the properties of Pawlak rough sets w.r.t. them. Secondly, by replacing equivalence classes in Pawlak rough approximations with neighborhoods, we introduce and study minimal neighborhood approximation operators on m-semilattices, and obtain some order properties of the set of all fixed points of minimal neighborhood approximation operators. Finally, we present the definition of fuzzy rough sets based on fuzzy coverings of m-semilattices, discuss some fundamental properties of fuzzy rough sets and investigate relations between fuzzy rough sets and fuzzy coverings.

Keywords: m-semilattice, Pawlak rough set, minimal neighborhood approximation operator, fuzzy covering, fuzzy rough set

DOI: 10.3233/IFS-152003

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2331-2338, 2016