A Novel Normalization Method for Using in Multiple Criteria Decision Analysis

Abstract

A typical multi-criteria decision analysis (MCDA) problem aims to rank a set of alternatives according to a set of criteria. The problem deals with selection of criteria, determination of criteria weights, normalization of criteria scores and aggregation of normalized criteria scores. The focus of this paper is on the normalization method. Most MCDA methods (e.g., AHP and TOPSIS) use a linear normalization method. Its main drawback is that the “magnitudes” of the normalized criteria scores of different criteria are different in terms of average. The difference in magnitude actually changes the relative importances of criteria so that the final rankings of alternatives may not appropriately reflect the preference of decision makers. To address this issue, a novel normalization method is proposed. The proposed normalization method uses a Gaussian value function to transform the criteria scores to interval (0, 1). The parameters of the value function are determined so that the average and variance of the normalized criteria scores are equal to pre-specified constants. A real-world dataset is used to illustrate the advantages of the proposed normalization method.