A data envelopment analysis (DEA)-based method for rule reduction in extended belief-rule-based systems

Rule reduction is one of the research objectives in numerous successful rule-based systems. In some analyses, too many useless rules may be a concern in a rule-based system. Although rule reduction has already attracted wide attention to optimise the performance of the rule-based system, the extended belief-rule-based system (EBRBS), which is an advanced rule-based system developed from the belief rule-based system (BRBS) recently, still lacks methods to reduce rules. This study focuses on the rule reduction of EBRBS and introduces data envelopment analysis (DEA) to evaluate the efficiency of each rule in an extended belief-rule-based (EBRB). However, two challenges must be addressed. First, a measure of the extended belief rule's efficiency value must be given because it is the foundation of rule reduction. Second, a novel decision-making-unit (DMU) must be constructed using the efficiency value of the extended belief rules to build a bridge for EBRBS and DEA. Therefore, the concepts of contribution degree and the extended belief rule-based DMU are introduced in the present study for the first time to propose a DEA-based rule reduction method. Moreover, the classic CCR model, which is identification engine of the rule reduction method, is applied to calculate the efficiency value of the extended belief rule and finally achieve the compact structure of an EBRB. Two case studies on regression and classification problems are performed to illustrate how efficiency of the DEA-based rule reduction method in promoting the performance of EBRBS. Comparison results demonstrate that the proposed rule reduction can downsize the EBRB and improve the accuracy of EBRBS. (C) 2017 Elsevier B.V. All rights reserved.