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

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Abstract

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.

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Acknowledgements

The authors would like to thank the Editor in Chief and reviewers for their thoughtful comments and valuable suggestions.

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Authors and Affiliations

  1. Bhalukdungri Jr. High School, Raigara, Purulia, WB, 723153, India

    Prasenjit Mandal

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

    A. S. Ranadive

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  1. Prasenjit Mandal
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Correspondence to Prasenjit Mandal.

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Mandal, P., Ranadive, A.S. Multi-granulation fuzzy decision-theoretic rough sets and bipolar-valued fuzzy decision-theoretic rough sets and their applications. Granul. Comput. 4, 483–509 (2019). https://doi.org/10.1007/s41066-018-0111-8

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