Transformation of bipolar fuzzy rough set models

In this paper, the notions of the union, the intersection, and the inverse of bipolar fuzzy approximation spaces are first introduced, respectively, and some related results are obtained. Then, the composition of bipolar fuzzy approximation spaces are proposed, and some properties are discussed. Finally, we give two examples to illustrate the applications of bipolar fuzzy rough set models' transformation in multiple criteria decision making. (C) 2011 Elsevier B.V. All rights reserved.