Utility Function

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

$$U = \left( \begin{array}{llll} U_{11} U_{12} \ldots U_{1m} \... ... \vdots \\ U_{n1} U_{n2} \ldots U_{nm} \end{array} \right)$$

where U_ij is the utility of the ith alternative task dealing with the jth objective.