Multiattribute decision making via identification of nondiagonal quadratic cost functions

This paper deals with multiattribute decision problems, using the approach based on the assumption of the existence of a (multiattribute) value/cost function. In particular, it addresses the problem of the identification of such a function on the basis of binary expressions for preferences and of other kinds of information provided by the decision maker. A general quadratic structure has been chosen for the cost function. In other words, in comparison with previous methods proposed in the literature, the present approach admits the possibility of ‘preferentially non-independent’ attributes. Some constraints (linear in parameters to be determined) are introduced to ensure the convexity of the quadratic function; hence the cost function identification gives rise to a linear programming problem.