The analysis of the quality of the results obtained with the methods of multi-criteria decisions

Abstract

For many decades we have been dealing with problems of multi-criteria decisions. Numerous methods have been developed in this field and new methods are continuously being created. In the light of a great number of methods currently proposed, it is difficult to gain a profound overview. Comparisons on the performance of various methods are done to a small extent only. When applying the methods, in some cases many mathematical operations are performed, which renders it impossible to sufficiently assess their effect with such a complexity. It is therefore aimed at analysing the peculiarities of several methods in a critical review and to give hints for possible consequences. The analysis is primarily concentrated on the normalisation of indices in the mapping to the interval [1; 0] or [1; ~ 0]. This includes linear functions (the relative difference and the calculation with interval boundaries) and non-linear functions (the hyperbolic function, the quadratic and cubic function, the square root and the logarithmic function). With the critical review, the possibility is offered to the decision maker to better assess the quality of his solution.