Correspondence:
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Corresponding author. Haidong Zhang, School of Mathematics and Computer Science, Northwest MinZu University, Lanzhou, Gansu, 730030, P. R. China. Tel./Fax: +86 9314512202; E-mail: lingdianstar@163.com.
Abstract: The dual hesitant fuzzy soft set is a generalized soft set by combining the dual hesitant fuzzy set and the soft set. Rough set theory is a powerful mathematical tool for dealing with uncertainty. Using a rough set theory, this paper develops a rough set approach to dual hesitant fuzzy soft set based on decision making problems. Firstly, by employing a dual hesitant fuzzy compatible relation, a new rough set model, called dual hesitant fuzzy compatible rough set, is first proposed, and some fundamental properties of this model are further examined. Then the concepts of roughness measure and approximate precision of a crisp set in dual hesitant fuzzy compatible approximation space are introduced and their basic properties are discussed. Furthermore, we present a rough set approach to dual hesitant fuzzy soft set based on decision making. Meanwhile, an example is provided to show the validity of this approach in dual hesitant fuzzy soft set based on decision making problems. Finally, by comparing the novel method with the decision making method based on intuitionistic fuzzy soft sets, we point out some advantages of the novel method.
