Methods of Evaluation and Improvement of Consistency of Expert Pairwise Comparison Judgments

The notion of consistency is used to evaluate the contradiction level of expert pairwise comparison judgments and their suitability for the purpose of calculation of weights of decision alternatives. Several consistency coefficients and criteria are used to measure inconsistency of a pairwise comparison matrix (PCM). Traditional approach to increase consistency of expert information is to organize a feedback with an expert. However, it is not always possible due to financial and time limitations. The paper deals with methods of improvement (increase) PCM consistency without participation of an expert. Computer simulation is used to provide a comparative study of these methods. It is shown that taking an inadmissibly inconsistent PCM, for example, with the consistency ratio equal to CR=0.2 or CR=0.3, methods of improvement PCM consistency help to decrease inconsistency up to admissible level CR≤0.1 for n≥5. Results reveal that these methods, unfortunately, are not always effective, that is, drawing near to admissible inconsistency does not ensure closeness to the vector of real weights of decision alternatives. Also an analysis of coefficients and criteria of consistency of expert pairwise comparison judgments depending on PCM properties and level of its consistency is carried out.