Multi-criteria evaluation of alternatives under conditions of uncertainty in the decision maker's preferences based on utility theory

The development of the methods of multi-criteria utility theory for the case of uncertainty in the decision-maker's preferences with respect to the value of evaluations by criteria and the importance of criteria is proposed. The main stages of the methods of the multi-criterion utility theory MAUT, MAVT are considered. Procedures for constructing fuzzy one criterion utility and value functions are proposed. An approach to determine the utility of the alternatives outcomes for crisp, interval and fuzzy estimates by criteria, as well as when describing the consequences by the probability distribution function is proposed. An approach to the scaling coefficients determination in conditions of uncertainty in the decision-maker's preferences is considered. As a result of applying the proposed approach with an additive utility or value function, a system of linear equations with fuzzy coefficients can be formed. To solve it, it is proposed to use an approach based on the representation of a system of fuzzy linear equations in the form of a set of systems of interval equations obtained by splitting fuzzy sets over $\alpha$-levels. The result of an external estimation of the solution set of an interval system of linear equations will allow us to establish the intervals of variation of the scaling coefficients under conditions of uncertainty in the decision maker's preferences and, furthermore, to obtain fuzzy scaling coefficients for multi-criteria utility and value functions.