Multi-granulation bipolar-valued fuzzy probabilistic rough sets and their corresponding three-way decisions over two universes

摘要: This article introduces general framework of multi-granulation bipolar-valued fuzzy (BVF) probabilistic rough sets (MG-BVF-PRSs) models in BVF approximation space over two universes. Four types MG-BVF-PRSs are established, by the four different conditional probabilities event. For constraints on parameters, we obtain kinds each type To find a suitable way explaining and determining these parameters kind MG-BVF-PRS, three-way decisions (3WDs) studied based Bayesian minimum-risk procedure, i.e., decision-theoretic set (MG-BVF-DTRS) approach. The main contribution this paper is twofold. One to extend (FPRS) MG-BVF-PRS model Another present an approach select modeling using process decision making under conditions risk.