METHOD FOR WEIGHTS CALCULATION BASED ON INTERVAL MULTIPLICATIVE PAIRWISE COMPARISON MATRIX IN DECISIONMAKING MODELS

Abstract

Context. The pairwise comparison method is a component of several decision support methodologies such as the analytic hierarchy and network processes (AHP, ANP), PROMETHEE, TOPSIS and other. This method results in the weight vector of elements of decision-making model and is based on inversely symmetrical pairwise comparison matrices. The evaluation of the elements is carried out mainly by experts under conditions of uncertainty. Therefore, modifications of this method have been explored in recent years, which are based on fuzzy and interval pairwise comparison matrices (IPCMs).
 Objective. The purpose of the work is to develop a modified method for calculation of crisp weights based on consistent and inconsistent multiplicative IPCMs of elements of decision-making model.
 Method. The proposed modified method is based on consistent and inconsistent multiplicative IPCMs, fuzzy preference programming and results in more reliable weights for the elements of decision-making model in comparison with other known methods. The differences between the proposed method and the known ones are as follows: coefficients that characterize extended intervals for ratios of weights are introduced; membership functions of fuzzy preference relations are proposed, which depend on values of IPCM elements. The introduction of these coefficients and membership functions made it possible to prove the statement about the required coincidence of the calculated weights based on the “upper” and “lower” models. The introduced coefficients can be further used to find the most inconsistent IPCM elements.
 Results. Experiments were performed with several IPCMs of different consistency level. The weights on the basis of the considered consistent and weakly consistent IPCMs obtained using the proposed and other known methods have determined the same rankings of the compared objects. Therefore, the results using the proposed method on the basis of such IPCMs do not contradict the results obtained for these types of IPCMs using other known methods. Rankings by the proposed method based on the considered highly inconsistent IPCMs are much closer to rankings based on the corresponding initial undisturbed IPCMs in comparison with rankings obtained using the known FPP method. The most inconsistent elements in the considered IPCMs are found.
 Conclusions. The developed method has shown its efficiency, results in more reliable weights and can be used for a wide range of decision support problems, scenario analysis, priority calculation, resource allocation, evaluation of decision alternatives and criteria in various application areas.