A balanced dematel theory with normalized indirect relation matrix

The generalized DEMATEL theory pointed out that the results of the traditional DEMATEL theory are always unbalanced and unfair, since their indirect relations are always far greater than their responding direct relations, respectively, it can be improved by using an external shrinkage coefficient of the indirect relation matrix of a DEMATEL. However, on other contrary, the indirect relations sometimes may be smaller than their corresponding direct relations respectively, it is still unbalanced, and it can be not improved by using the above-mentioned method. In this paper, Liu’s balanced coefficient was proposed, which can be used to detect any DEMATEL whether it is balanced; furthermore, we proved that if the internal shrinkage coefficient is smaller than 0.5, then its indirect relation is smaller than its direct relation. For overcoming this drawback, we propose a new method, called the balanced DEMATEL theory, by normalizing the indirect relation matrix as the direct relation matrix has been done. For any cases, according to Liu’s validity index, we can find that the performance of the new method is better than that of the generalized DEMATEL theory. Some important properties of this new theory were discussed, and a simple data was also provided in this paper to illustrate the advantages of the proposed theory.