Bayesian rough set model: A further investigation

Bayesian rough set model (BRSM), as the hybrid development between rough set theory and Bayesian reasoning, can deal with many practical problems which could not be effectively handled by original rough set model. In this paper, the equivalence between two kinds of current attribute reduction models in BRSM for binary decision problems is proved. Furthermore, binary decision problems are extended to multi-decision problems in BRSM. Some monotonic measures of approximation quality for multi-decision problems are presented, with which attribute reduction models for multi-decision problems can be suitably constructed. What is more, the discernibility matrices associated with attribute reduction for binary decision and multi-decision problems are proposed, respectively. Based on them, the approaches to knowledge reduction in BRSM can be obtained which corresponds well to the original rough set methodology.