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

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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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Acknowledgements

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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Authors and Affiliations

  1. Bhalukdungri Jr. High School, Raigara, Purulia, W.B., 723153, India

    Prasenjit Mandal

  2. Department of Pure and Applied Mathematics, Guru Ghasidas University, Bilaspur, C.G., India

    A. S. Ranadive

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  1. Prasenjit Mandal
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  2. A. S. Ranadive
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Correspondence to Prasenjit Mandal.

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Prasenjit Mandal and A. S. Ranadive declare that there is no conflict of interest.

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Communicated by V. Loia.

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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

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