A non-linear utility theory with multiple objectives

The aim of this paper is to make optimum several objectives at the same time which would enable a measurement of utility for several possible alternatives. The problem is solved if a strong or weak dominance exists between the alternatives, otherwise a set of incomparable alternatives would be present. Therefore, indifference curve analysis offers the outcome but as these indifference loci are difficult to determine only the characteristics of this analysis are maintained, viz. decreasing marginal utility, non-linearity and even non-convexity. Indifference and reference point theory with the Minkowski min–max-metric only respond to these characteristics. Also the problem of generating alternatives during the process is taken into consideration.