DEVELOPMENT OF A METHOD FOR THE COMPLETION OF MATRICES OF PAIRED COMPARISONS OF MULTIPLE PREFERENCES BASED ON THE CONSISTENCY INDEX

Expert evaluation is a methodology that includes various methods to solve complex and poorly formalized problems. One of the most common and promising methods is the analytical hierarchy process developed by T. Saati. Despite such advantages as independence from the application area, simplification an expert work by pairwise comparison matrices usage, basing on human experience, a convenient rating scale and the inconsistency of expert opinion control, the analytical hierarchy process has several disadvantages. One of them is the lack of the ability to interact with incomplete expert information. To modify the AHP an algorithm of matrix completion based on maximizing the consistency index is considered. As an indicator of consistency, not the index of cardinal consistency proposed by Saati, but based on the search for non-transitivity among the triples of preferences one was taken. Based on the maximization of the proposed index of consistency, a method of completion matrices of pairwise comparisons of ordinal preferences containing incomplete expert information was considered. Also, a survey of experts was conducted and matrices of pairwise comparisons were obtained. Then, by using randomized method, matrices were transformed into incomplete ones and completed by the method given. A comparison of the consistency indices of the initial and transformed matrices of pairwise comparisons was made.

Authors: P. L. Lyubkin

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Keywords: Expert evaluation, analytical hierarchy process, pairwise comparison matrices, consistency index, matrices completion, ordinal preferences

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