A utility function transforms an outcome into a numerical value and measures the worth of an outcome. The utility of an outcome may be negative or positive. This utility function may be a simple table, a linear function, or a more complex function. The outcome matrix is converted to the utility matrix using the utility function.

Let *U* be the utility matrix

where *U*_{ij} is the utility of the *ith* alternative task
dealing with the *jth* objective.