A heuristic algorithm for attribute reduction of decision-making problem based on rough set

As a basic problem in rough set (RS) theory, the attribute reduction of decision-making problem is to remove superfluous attributes from problem representation (i.e. decision tables) while preserving the consistency of classifications the original decision system provides. Identifying all reductions or the minimal reductions of a decision-making problem is already proved to be NP-hard. Therefore, heuristic rules are needed to solve this kind of NP-hard problem with higher efficiency during the reduction finding process. In this paper, we introduce some concepts of rough set relevant to reduction and present an algorithm combining discernibility matrix (DM) and principal component analysis (PCA) as heuristic knowledge to find the reduction.