Abstract
This article introduces general framework of multi-granulation bipolar-valued fuzzy (BVF) probabilistic rough sets (MG-BVF-PRSs) models in multi-granulation BVF probabilistic approximation space over two universes. Four types of MG-BVF-PRSs are established, by the four different conditional probabilities of BVF event. For different constraints on parameters, we obtain four kinds of each type MG-BVF-PRSs over two universes. To find a suitable way of explaining and determining these parameters in each kind of each type MG-BVF-PRS, three-way decisions (3WDs) are studied based on Bayesian minimum-risk procedure, i.e., the multi-granulation BVF decision-theoretic rough set (MG-BVF-DTRS) approach. The main contribution of this paper is twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-BVF-PRS model over two universes. Another is to present an approach to select parameters in MG-BVF-PRS modeling by using the process of decision making under conditions of risk.
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The authors would like to thank the Associate Editor and reviewers for their thoughtful comments and valuable suggestions. Some tables and figures are directly benefitted from the reviewers comments.
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Prasenjit Mandal and A. S. Ranadive declare that there is no conflict of interest.
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Mandal, P., Ranadive, A.S. Multi-granulation bipolar-valued fuzzy probabilistic rough sets and their corresponding three-way decisions over two universes. Soft Comput 22, 8207–8226 (2018). https://doi.org/10.1007/s00500-017-2765-6
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DOI: https://doi.org/10.1007/s00500-017-2765-6