A Novel Method for Fuzzy Measure Identification

Abstract

Fuzzy measure and Choquet integral are effective tools for handling complex multiple criteria decision making (MCDM) problems in which criteria are inter-dependent. The identification of a fuzzy measure requires the determination of 2(n) - 2 values when the number of criteria is n. The complexity of this problem increases exponentially, which makes it practically very difficult to solve. Many methods have been proposed to reduce the number of values to be determined including the introduction of new special fuzzy measures like the lambda -fuzzy measures. However, manipulations of the proposed methods are difficult from the aspects of high data complexity as well as low computation efficiency. Thus, this paper proposed a novel fuzzy measure identification method by reducing the data complexity to n(n - 1)/2 and enhancing the computation efficiency by leveraging a relatively small number of variables and constraints for linear programming. The proposed method was developed based on the evaluation of pair-wise additivity degrees or interdependence coefficients between the criteria. Depending on the information being provided by decision-makers on the individual density of each criterion, the fuzzy measure can be constructed by solving a simple system of linear inequalities or a linear programming problem. This novel method is validated through a supplier selection problem which occurs frequently in real-world decision-making problems. Validation results demonstrate that the newly-proposed method can model real-world MCDM problems successfully.