A non-heuristic multicriteria decision-making method with verifiable accuracy and reliability

Multicriteria decision making (MCDM) methods are widely used in decision making practice. However, these methods are heuristic: they are based on some rules, the effectiveness and validity of which cannot be strictly proved, and it is unknown exactly how trustworthy their outputs reflect Decision-maker’s judgements. Such methods can generate different outputs, using the same inputs, and it is impossible to select the more correct method from the available ones – this is the subject of the decision-making paradox. In this article, we focus on the possibility to construct a non-heuristic MCDM method, whose accuracy and reliability can be verified. We base the proposed method on two new ideas on how to construct a pairwise comparison (PC) matrix for a multi-criteria decision-making problem with several criteria and alternatives, and how to correctly derive information from this matrix. We show that it is possible (i) to estimate the objective uncertainty in the PC-matrix information with respect to each alternative and (ii) to estimate the reliability of the rankings. The non-heuristic MCDM method based on these ideas allows to verify the accuracy and reliability of Decision-maker’s judgements on MCDM problems, and has clear anti-reversal guarantees. The software implementing the method is freely available online at http://QSP.decisiontool.net.