Comparison of fuzzy numbers in decision-making problems

The paper deals with decision-making problems, when a decision maker receives information about possible pay-off as a result of a strategy selection. This information can be given as a fuzzy number and the problem of its comparison appears. A specific character of the problem is a main factor to choose the method of the fuzzy numbers comparison. In this paper an approach of comparing fuzzy numbers has been proposed, it's based on the comparison of $\alpha$-cuts. These $\alpha$-cuts are segments. During the comparison of the segments, each segment can contain a merit value; one of the decision-making criteria is chosen (Wald's maximin model, Regret theory models, Routh–Hurwitz stability criterion etc.). The results of the comparison are averaged out. Fuzzy numbers are compared according to these mean values. According to geometrical interpretation which has been given, the comparison of fuzzy numbers is equivalent to the comparison of figures' areas. These areas are formed by graphics of membership functions of the fuzzy numbers. As an example trapezoidal and bell-shaped fuzzy numbers are examined.