Three-way Decisions with Rough Membership Functions in Covering Approximation Space

Article type: Research Article

Authors: Yang, Bin | Hu, Bao Qing^{; *} | Qiao, Junsheng

Correspondence: [*] Address for correspondence: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China.

Abstract: Rough membership functions in covering approximation space not only give numerical characterizations of covering-based rough set approximations, but also establish the relationship between covering-based rough sets and fuzzy covering-based rough sets. In this paper, we give a new method to discuss three-way decisions with rough membership functions in covering approximation space. Firstly, we introduce three new types of rough membership functions and study their properties. And then, relationship between a covering and its derived fuzzy β-covering is investigated by using rough membership functions. In addition, we study the relationship among the four types of rough membership functions. Finally, a novel type of graded covering-based rough set model is proposed on the basis of rough membership function. And, as an application, its corresponding three-way decisions in incomplete decision systems are investigated.

Keywords: Fuzzy β-covering, Graded covering-based rough set, Neighborhood, Rough membership function, Three-way decisions

DOI: 10.3233/FI-2019-1780

Journal: Fundamenta Informaticae, vol. 165, no. 2, pp. 157-191, 2019