Revised DEMATEL: Resolving the Infeasibility of DEMATEL

Decision Making Trial and Evaluation Laboratory (DEMATEL) has been applied in many situations, such as marketing strategies, control systems, safety problems, developing the competencies of global managers and group decision making. It has been incorporated into other methods such as Analytical Network Process (ANP), Multiple Criteria Decision Making (MCDM), fuzzy set theory, etc., to vitalize these traditional methods and explore new applications for the hybrid methods. DEMATEL models the influences of components of a system with an initial direct relation matrix. Influences of components can ripple transitively to other components, which is modeled by raising the initial direct relation matrix to powers. The total influence is computed by summing up matrices of all powers based on the assumption that the matrix raising to the power of infinity would converge to zero. The current paper shows that raising the initial relation matrix to the power of infinity may not converge to zero and hence total influence may not converge. The current paper also shows that our revised DEMATEL guarantees that the initial direct-relation matrix to infinite power will converge to zero and the total influence can be obtained accordingly. The newly developed approach is illustrated with numerical examples.