Some equations to identify the threshold value in the DEMATEL method

Abstract

DEMATEL technique is a graphical representation method to deal with complex systems. The final analyzed cause and effect categorization would be fundamentally dependent on the threshold value setting. This research is intended to present some mathematical models for calculating the threshold value in the DEMATEL method. The min(max) operator has been intentionally used for considering three equations to identify the threshold value. Additionally, the proposed mathematical equations are gradually developed to gain more useful data to yield a threshold value as well. Particularly, the expert’s initial scoring for building the primary matrix would also be applied in one equation. Results show eliciting an expert’s opinions regarding the value of a threshold value determination leads to setting relatively high thresholds. But, there would be an equation which takes advantage of more data derived from the total influence matrix T. Moreover, a span of different threshold values is gained by making use of the Hamacher t-conorms operator which especially would cause better complexity management of the final total matrix T based on expert’s opinions. As a contribution to this research, threshold value determination is developed mathematically by making use of the direct data gained by the total matrix T. Besides combining data derived from total matrix T, the initial influence direct matrix given by experts, a simpler aggregating procedure and no need for statistical information compared to special Lenth’s method hints at this research’s novelty as well.