Constructing Quadratic, Polynomial, and Separable Objective Functions

A model for constructing quadratic, polynomial, and separable objective functions from interviewing experts is considered. The person interviewed is presented a set of incomplete alternatives (vectors of target variables, with one coordinate not being fixed) and is asked to complete these alternatives (to adjust this one coordinate) to make these vectors equivalent in preference to some given reference vector. The objective function is determined by the indifference hypersurface fitted to the equivalent vectors constructed. Besides formal properties of the model and its regression-like extensions, computer experiments on constructing an objective function of German economic policy in four target variables (inflation, unemployment, GNP growth, and public debt) are briefly reported for illustration.