On Some Surprising Application of Graphs in Decision Making: Pairwise Comparisons

In many multiple criteria decision making problems (in particular in the case of group expert decisions) the Pairwise Comparison Matrices (PCM) are used. In almost all the cases such matrices are inconsistent (i.e. they do not satisfy some axioms). In such a situation, it is necessary to find a consistent matrix that is closest to the given one with respect to some distance measure. In the case of the measure L₂, the resulting optimization problem is non-convex and multiple local optima are possible. In the talk some results for the case of the measure L_∞ will be presented. Rather surprisingly, after using the logarithmic transformation, the subproblems become equivalent to the instances of the Shortest Path Problem (some of which can be divergent). Using this property we propose effective method of deriving the consistent PCM.

This is a joint work with Janos Fulop.