Centroidous Method for Determining Objective Weights

Abstract

When using multi-criteria decision-making methods in applied problems, an important aspect is the determination of the criteria weights. These weights represent the degree of each criterion’s importance in a certain group. The process of determining weight coefficients from a dataset is described as an objective weighting method. The dataset considered here contains quantitative data representing measurements of the alternatives being compared, according to a previously determined system of criteria. The purpose of this study is to suggest a new method for determining objective criteria weights and estimating the proximity of the studied criteria to the centres of their groups. It is assumed that the closer a criterion is to the centre of the group, the more accurately it describes the entire group. The accuracy of the description of the entire group’s priorities is interpreted as the importance, and the higher the value, the more significant the weight of the criterion. The Centroidous method suggested here evaluates the importance of each criterion in relation to the centre of the entire group of criteria. The stability of the Centroidous method is examined in relation to the measures of Euclidean, Manhattan, and Chebyshev distances. By slightly modifying the data in the original normalised data matrix by 5% and 10% 100 and 10,000 times, stability is examined. A comparative analysis of the proposed Centroidous method obtained from the entropy, CRITIC, standard deviation, mean, and MEREC methods was performed. Three sets of data were generated for the comparative study of the methods, as follows: the mean value for alternatives with weak and strong differences and criteria with linear dependence. Additionally, an actual dataset from mobile phones was also used for the comparison.