Unsupervised Identification for 2-Additive Capacity by Principal Component Analysis and Kendall’s Correlation Coefficient in Multi-Criteria Decision-Making

With the Multi-Criteria Decision-Making (MCDM) problems becoming increasingly complex, traditional MCDM methods cannot effectively handle ambiguous, incomplete, or uncertain data. While several novel types of MCDM methods have been proposed to address this limitation, they fail to consider the potentially complex interactions among decision criteria. An effective capacity identification methodology is definitely needed to conquer this issue. In this paper, we develop a novel unsupervised method for identifying 2-additive capacities by means of Principal Component Analysis (PCA) and Kendall’s correlation coefficient. During the process, some significant results are achieved. Firstly, the Shapley values of decision criteria are derived by using the PCA, through a combination of the variance contribution rate of each Principal Component (PC) and its corresponding eigenvector. Secondly, Kendall’s correlation coefficient stemmed from the decision data created to help identify the Shapley interaction index for each pair of criteria by unsupervised learning. The optimization model equipped with a new form of monotonicity conditions is then established to further determine the optimal Shapley interaction index. With these two kinds of indices, a desired monotone 2-additive capacity is finally identified in an objective and efficient manner. Numerical experiments demonstrate that our proposal can adequately consider the importance of criteria and accurately identify the types of Shapley interaction indices between criteria, and is thus able to produce more convincing and logical results compared with other unsupervised identification methods.