Abstract: An interval UTA method was proposed for inferring interval utility functions from a partial preorder of alternatives evaluated on multiple criteria, which was an extension of the well-known UTA method capable to handle the interval evaluation data. Firstly, according to the original UTA method, the interval attribute values of all reference options were transformed into the ranges of utility, namely, the utility intervals. Next, the overall utility intervals were calculated using the arithmetic operations of interval number. A linear programming model was constructed based on the satisfaction degree of decision maker utilizing the mid-point and half-width of interval numbers. After the total error value was obtained, a quadratic programming model was established in the post-optimization step, where the objective function was the minimum utility variance of all nodes along all criteria. The obtained utility values of all nodes were used to calculate the overall utility intervals and ranking of alternatives under evaluation. Numerical example showed that the alternatives could effectively ranked using the proposed interval UTA method, which was compatible with the preference information of decision maker.

Key words: UTA method, multiple criteria decision, utility value, interval number, the satisfaction degree