Bipolar-Valued Rough Fuzzy Set and Its Applications to the Decision Information System

In this paper, first, relationship between bipolar-valued fuzzy set and fuzzy set with its extensions is discussed. Second, a new order relation about bipolar-valued fuzzy sets is introduced. Contrary to the existing YinYang order relation about bipolar-valued fuzzy sets, which focuses on the equilibrium monotonicity, the new proposed order relation is concerned with preference monotonicity. And then, some new operations and related properties about the new defined order relation are presented. Third, by combining bipolar-valued fuzzy set with the rough set theory, the concept of the bipolar-valued rough fuzzy set is developed, which is the first attempt to consider inconsistent bipolarity into rough set theory. Particularly, by introducing two new operations to the rough set theory, the widely existing information losing problem in the computation process is solved. Furthermore, parameter-related and parameter-free rough degrees about the bipolar-valued fuzzy sets in a crisp approximation space are introduced. Finally, the bipolar-valued fuzzy decision information system is given; then, both the attribute reduction method and the knowledge discovery method based on the proposed roughness degree are presented. An example is included to show the feasibility and potential of the obtained theoretical results.