A Heuristic Algorithm for Generating Decision Rules in Variable Precision Rough Set Models

Abstract

In this paper, we propose a heuristic algorithm to extract decision rules based on variable precision rough set models (VPRS models). The VPRS models provides a theoretical basis of regarding probabilistic / inconsistent information in the framework of rough set theory. The main idea of our algorithm is based on construction of suitable β-lower approximations by giving up to discern some discernible objects that belong to different decision classes each other. All decision rules extracted by our algorithm are guaranteed that the certainty of all extracted decision rules are equal to or higher than the predefined threshold of certainty. I. I NTRODUCTION Extraction of decision rules is an important application of rough set theory (4), (5) from a viewpoint of data analysis. Variable precision rough set models (for short, VPRS models) proposed by Ziarko (8) provides a theoretical basis of regard- ing probabilistic / inconsistent information in the framework of rough set theory. In this paper, we propose a heuristic algorithm to extract decision rules based on the VPRS models. The main idea of our algorithm is based on construction of suitable β- lower approximations by giving up to discern some discernible objects that belong to different decision classes each other. All decision rules extracted by our algorithm are guaranteed that the certainty of all extracted decision rules are equal to or higher than the predefined threshold of certainty. The rest of this paper is organized as follows. In Section II, we review Pawlak's rough set theory and the VPRS models as the background of this paper. In Section III, we introduce a heuristic algorithm to extract decision rules based on the VPRS models, and describe small examples to explain how the proposed algorithm works. We discuss a few properties of the proposed algorithm in Section IV and finally conclude this paper in Section V.