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

Document Type: Research Paper

Authors

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

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

Abstract

This article introduces a general framework of multi-granulation fuzzy probabilistic rough
sets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over two
universes. Four types of MG-FPRSs are established, by the four different conditional probabilities
of fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSs
over two universes. To find a suitable way of explaining and determining these parameters in each
kind of each type MG-FPRS, three-way decisions (3WDs) are studied based on Bayesian minimum-risk
procedure, i.e., the decision-theoretic rough set (DTRS) approach. The main contribution of this paper
is twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-FPRS model over two universes.
Another is to present an approach to select parameters in MG-FPRS modeling by using the process of
decision-making under conditions of risk.

Keywords


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