A condition number based group correspondence method for multi-criteria group decision making

Abstract

The correspondence between decision parameters and group assessments is a new and important concept in multi-criteria group decision making (MCGDM), named as group correspondence. It characterizes the degree to which the changes in group assessments correspond to the changes in decision parameters. In the existing studies, however, group correspondence is rarely considered in MCGDM. In this paper, a group correspondence method is developed based on condition numbers. Through the analysis of the difference between sensitivity and group correspondence in MCGDM, the necessity of proposing group correspondence is demonstrated. The formal definition of group correspondence in MCGDM is first presented, and then its measurement is constructed based on the condition number of a matrix. Moreover, a feedback mechanism is developed to help accelerate the convergency of the group correspondence. The identification and suggestion rules for the two steps of aggregation of the assessments are included in the feedback mechanism to suggest that the specific decision makers renew their identified assessments and weights of the criteria. The process of the proposed method for MCGDM is then designed. A control mode selection problem for a manufacturing enterprise located in Changzhou, Jiangsu, China is analyzed using the proposed method to demonstrate its validity and applicability.