A generalized DEMATEL theory with a shrinkage coefficient for an indirect relation matrix

¹ Department of Biomedical Informatics, Asia University, Taichung 41354, Taiwan
² Big Data Research Center & School of Management School of Health Care Administration, Taipei Medical University, Taipei 11031, Taiwan
³ Department of Finance, Ling Tung University, Taichung 40852, Taiwan
⁴ Graduate School of Business Administration, Fu Jen Catholic University, Xinzhuang Dist., New Taipei City 24205, Taiwan

^a Corresponding author : ycou@teamail.ltu.edu.tw

Abstract

In this paper, a novel decision-making trial and evaluation laboratory (DEMATEL) theory with a shrinkage coefficient of indirect relation matrix is proposed, and a useful validity index, called Liu’s validity index, is also proposed for evaluating the performance of any DEMATEL model. If the shrinkage coefficient of an indirect relation matrix is equal to 1, then this new theory is identical to the traditional theory; in other words, it is a generalization of the traditional theory. Furthermore, the indirect relation is always considerably greater than the direct one in traditional DEMATEL theory, which is unreasonable and unfair because it overemphasizes the influence of the indirect relation. We prove in this paper that if the shrinkage coefficient is equal to 0.5, then the indirect relation is less than its direct relation. Because the shrinkage coefficient belongs to [0.5, 1], according to Liu’s validity index, we can find a more appropriate shrinkage coefficient to obtain a more efficient DEMATEL method. Some crucial properties of this new theory are discussed, and a simple example is provided to illustrate the advantages of the proposed theory.