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

Yang Bin, Hu Bao Qing, Quiao Junsheng

Fundamenta Informaticae

2019

Vol. 165, nr 2

157--191

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.