A Novel Normalization Method for Using in Multiple Criteria Decision Analysis A typical multicriteria 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 xe2x80x9cmagnitudesxe2x80x9d 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 prespecified constants. A realworld dataset is used to illustrate the advantages of the proposed normalization method.

Using a segmenting description approach in multiple criteria decision aiding Abstract   We propose a new method for analyzing a set of parameters in a multiple criteria ranking method. Unlike the existing techniques, we do not use any optimization method, instead incorporating and extending a Segmenting Description (SD) approach. The algorithm rewrites a set of initial inequalities into an equivalent SD system by means of three fundamental operations in a way that makes it possible to either easily analyze all feasible solutions or identify all sources of inconsistency. While considering a valuebased preference disaggregation method, we demonstrate the usefulness of the introduced method in a multipurpose decision analysis exploiting a system of inequalities that models the Decision Makerxe2x80x99s (DMxe2x80x99s) preferences. We focus on the contexts where informative results can be obtained through the analysis of (in)feasibility of such systems. Specifically, we discuss how SD can be applied for verifying the consistency between the revealed and estimated preferences as well as for identifying the reasons of potential incoherence. Moreover, we employ the method for conducting robustness analysis, i.e., discovering a set of all compatible parameter values and verifying the stability of suggested recommendation in view of multiplicity of feasible solutions. In addition, we make clear its suitability for generating arguments about the validity of outcomes and the role of particular criteria. Overall, the SD approach confirms its usefulness in analyzing the relationships between the DMxe2x80x99s preference information, the compatible parameters of an assumed model, and the valuedriven ranking procedure. We also discuss the favourable characteristics of the proposed method enhancing its suitability for use in Multiple Criteria Decision Aiding. These include possibility of studying any system of inequalities without an objective function, keeping in memory an entire process of transforming a system of inequalities that makes identification of potential incoherence straightforward, and avoiding the need for processing the inequalities contained in the basic system which is subsequently enriched with some hypothesis to be verified. The latter is substantial for saving time when a multitude of hypotheses need to be checked in the same conditions. The applicability and the advantages of using the proposed method in the decision aiding context are clearly exemplified on a numerical study.