Analysis of DEMATEL Balance and Variation via Liu’s Integrated Validity Index

Abstract

This paper introduces a novel integrated validity index for evaluating and comparing the balance-variation order pairs of different Decision-Making Trial and Evaluation Laboratory (DEMATEL) methods. Specifically, when one DEMATEL model exhibits higher balance and lower variation, while another displays the opposite, the proposed index—combining Liu’s balanced coefficient and Liu’s variation coefficient—offers a comprehensive assessment of their validity. Using this new metric, three DEMATEL approaches with the same direct relational matrix are analyzed: traditional DEMATEL, shrinkage DEMATEL, and balance DEMATEL. A comparative validity experiment demonstrates that balance DEMATEL outperforms the other methods, followed by shrinkage DEMATEL, which exhibits superior performance over the traditional DEMATEL. These findings highlight the effectiveness of the proposed validity index in distinguishing and assessing DEMATEL variations, providing valuable insights for decision-making model optimization.