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.
Highlights
A decision-making trial and evaluation laboratory (DEMATEL) was developed by Gabus and Fontela [1] and Fontela and Gabus [2] for resolving complex and difficult problems
DEMATEL has been widely used as one of the most effective tools for solving cause–effect relationships among evaluation factors [3-10], but the indirect relation of a DEMATEL model is always markedly greater than its direct relation, which is unreasonable and unfair because it overemphasizes the influence of the indirect relation
To overcome this drawback, we propose an external shrinkage coefficient for constructing a reduced indirect relation matrix, such that the new indirect relation matrix is less than its direct relation matrix, and for evaluating the performance of any DEMATEL model
Summary
A decision-making trial and evaluation laboratory (DEMATEL) was developed by Gabus and Fontela [1] and Fontela and Gabus [2] for resolving complex and difficult problems. DEMATEL has been widely used as one of the most effective tools for solving cause–effect relationships among evaluation factors [3-10], but the indirect relation of a DEMATEL model is always markedly greater than its direct relation, which is unreasonable and unfair because it overemphasizes the influence of the indirect relation. To overcome this drawback, we propose an external shrinkage coefficient for constructing a reduced indirect relation matrix, such that the new indirect relation matrix is less than its direct relation matrix, and for evaluating the performance of any DEMATEL model. We propose a useful validity index, called Liu’s validity index, for evaluating the performance of any DEMATEL model. A generalized DEMATEL is derived and shown to be more useful and effective than previous DEMATEL models
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