Grey relational analysis and radial basis function network for determining costs in learning sequences Yi-Chung Hu Department of Business Administration, Chung Yuan Christian University, Chung-Li 32023, Taiwan, ROC Abstract There is a competence set consisting of ideas, knowledge, information, and skills for solving a decision problem. In order to effectively acquire the needed skills in the competence set to solve the problem, finding appropriate learning sequences of the needed skills for decision makers should be taken into account. However, how to determine the learning cost of learning one skill to another skill plays a critical role for generating learning sequences. For this, the paper aims to propose an effective method to estimate the learning cost between any two skills by using the grey relational analysis and a radial basis function network. A computer simulation with an integer programming method is employed to demonstrate that it is possible to facilitate the acquisition of single skills by considering a set of useful compound skills. This indicates the effectiveness of the proposed method. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Grey relational analysis; Radial basis function network; Learning sequences; Integer programming 1. Introduction There is a competence set consisting of ideas, knowledge, information, and skills for solving a decision problem [1]. When decision makers have acquired the needed competence set and are proficient in it, they will be comfortable and confident in making decisions [2,3]. Otherwise, they must acquire the needed competence set to solve the problem. In order to acquire a needed set of skills to cope with a decision they face, finding appropriate learning sequences of acquiring needed skills is very necessary. Skills can be roughly classified into two types: one is single skills, and the other is compound skills. A com- pound skill represents a collection of single skills that might be acquired by decision makers. A compound skill may facilitate the acquisition of other single skills [4,5]. For instance, the courses ‘‘marketing management’’, ‘‘financial management’’ and ‘‘business policy’’ are needed single skills for obtaining a bachelor’s degree of business administration, and are denoted by m, f and b, respectively. When both ‘‘marketing management’’ and ‘‘financial management’’ have been acquired or learnt, these two single skills form a compound skill, denoted by m ^ f. Usually, whether m or f has been acquired or not for an undergraduate student can be 0096-3003/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2006.05.162 E-mail address: ychu@cycu.edu.tw Applied Mathematics and Computation 184 (2007) 291–299 www.elsevier.com/locate/amc