Multi-granulation fuzzy decision-theoretic rough sets and bipolar-valued fuzzy decision-theoretic rough sets and their applications

This paper investigates the decision-theoretic rough set (DTRS) approach in the frameworks of multi-granulation fuzzy and bipolar-valued fuzzy (BVF) probabilistic approximation spaces, respectively. By integrating fuzzy probability and BVF probability into the Bayesian decision procedure, we get four types of model of multi-granulation fuzzy decision-theoretic rough set (MG-FDTRS) approach and multi-granulation bipolar-valued fuzzy decision-theoretic rough set (MG-BVF-DTRS) approach. Our four types of model of the MG-FDTRS and the MG-BVF-DTRS approaches are mainly based on computation of the four different conditional probabilities within the frameworks of multi-granulation fuzzy and BVF probabilistic approximation spaces, respectively. The main contribution of this paper is twofold. One is to extend the fuzzy decision-theoretic rough set (FDTRS) approach to the MG-FDTRS and the MG-BVF-DTRS approaches. Another is to address its applicable ability as it is applied to deal with the multi-source fuzzy and BVF probabilistic decision systems. An example is included to show the feasibility and potential results obtained.