Soft Computing

, Volume 22, Issue 24, pp 8207–8226 | Cite as

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

  • Prasenjit MandalEmail author
  • A. S. Ranadive
Methodologies and Application


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.


Rough 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.

Compliance with ethical standards

Conflict of interest

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

Ethical approval

This article does not contain any study performed on humans or animals by the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Bhalukdungri Jr. High SchoolRaigara, PuruliaIndia
  2. 2.Department of Pure and Applied MathematicsGuru Ghasidas UniversityBilaspurIndia

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