Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC and SD

The comparative analysis of objective methods for determining the weights of criteria in the problems of multi-criteria decision-making is carried out. It is shown that the use of methods for determining the weights of criteria, based on formal processing of the decision matrix (Entropy, CRITIC, Standard deviation) for MCDM problems in some cases is not correct. It is demonstrated that the Entropy weighting method (EWM) is highly sensitive to evaluation of probabilities of states based on the decision matrix. For the Entropy method two modifications of estimation of probabilities of states are proposed that partially eliminate the contradictions of the basic EWM method. The first modification (EWM.df) is based on a statistical approach and it estimates the probabilities of states based on attribute distribution function. The second modification (EWM.dsp) estimates the probabilities of states based on the relative dispositions of attributes. Two options both have their supporting rationale. The analysis of integrated weighing methods is carried out and various options for aggregation of weights are given. An integrated EWM-Corr-method is proposed which allows to re-allocate the weights obtained by the Entropy method among correlated criteria.