A novel DEMATEL theory based on Liu's polytomous ordering theory

The most important issue in DEMATEL theory is how to obtain a reliable initial direct relation matrix with order n, the traditional theory obtains it by using the pair-wise comparison method, in which, each respondent must answer n(n-1) times pair-wise comparisons of all of the direct influences, if n is a large number, the work of pair-wise comparing is becoming hard, time-consuming, and unreliable. In this paper, for overcoming above drawbacks, we replace the pair-wise comparison method with Liu's ordering theory to find the initial direct relation matrix. This new method without pair-wise comparing can be used for any order n, a simple example was also provided in this paper to illustrate the advantages of the proposed theory.