The Interactive Weighting Method Concerning Consistency, Inadequacy, Complementary and Supplementary Properties of Criteria

In most multicriteria decision-making methods, several options are ranked according to numerous criteria. In the decision-making process, experts often determine the importance weight of the criteria by comparing them to each other or with ideal solutions. With increasing criteria, the decision-making process becomes more complex, and the compatibility of judgments is reduced. Another problem is the inadequacy of criteria at different levels of the decision-making process. A high-level criterion can be considered, which includes several subcriteria. The subcriteria considered may not include all of the possible subcriteria because they could be unknown to decision-makers or could not be measured and used by decision-makers. Hence, the assumption that the importance weight of the subcriteria equals one (for example, in the analytic hierarchy process method) may not always be accurate. In this article, a new decision-making method is proposed based on Shapley's value that can extract the importance weight of criteria at different levels by considering the consistency between subcriteria. Additionally, an interactive top–down decision-making approach is presented for compatible judgments. The proposed method is applied to determine the importance weights of criteria in a sustainable supplier selection problem, and we show how the method could facilitate the extraction of the importance weight and address the inadequacy and dependency properties between the criteria.