
## Bayesian Approach To Rough Set

Tshilidzi Marwala and Bodie Crossingham University of the Witwatersrand Private Bag x3 Wits, 2050 South Africa e-mail: t.marwala@ee.wits.ac.za This paper proposes an approach to training rough set models using Bayesian framework trained using Markov Chain Monte Carlo (MCMC) method. The prior probabilities are constructed from the prior knowledge that good rough set models have fewer rules. Markov Chain Monte Carlo sampling is conducted through sampling in the rough set granule space and Metropolis algorithm is used as an acceptance criteria. The proposed method is tested to estimate the risk of HIV given demographic data. The results obtained shows that the proposed approach is able to achieve an average accuracy of 58% with the accuracy varying up to 66%. In addition the Bayesian rough set give the probabilities of the estimated HIV status as well as the linguistic rules describing how the demographic parameters drive the risk of HIV. 

## Introduction

Rough set theory (RST) was introduced by Pawlak (1991) and is a mathematical tool which deals with vagueness and uncertainty. It is of fundamental importance to artificial intelligence (AI) and cognitive science and is highly applicable to the tasks of machine 