Multi-granulation bipolar-valued fuzzy probabilistic rough sets and their corresponding three-way decisions over two universes
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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.
KeywordsRough set Fuzzy event Bipolar-valued fuzzy event Multi-granulation bipolar-valued fuzzy probabilistic rough set Three-way decisions
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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Conflict of interest
Prasenjit Mandal and A. S. Ranadive declare that there is no conflict of interest.
This article does not contain any study performed on humans or animals by the authors.
Informed consent was obtained from all individual participants included in the study.
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