A Multiplicative Method for Synthesizing Preference Ratings

Consider a discrete alternative multicriteria problem, in which the attractiveness of the alternatives is measured by absolute, ratio-scale preference ratings on a set of relevant criteria. We introduce a nonlinear, multiplicative functional form for combining the ratio-scale ratings to determine their overall priority ratings, which, depending on the preference information provided by the decision maker, can yield overall priority ratings that reflect situations of decreasing, constant or increasing marginal contributions to the achievement of the overall goal. Previous methods for combining priorities using a nonlinear functional form have either been based on interval-scale value function representations, or have assumed constant marginal contributions to the overall goal. As noted previously by other researchers, our method the overall priorities maintain the ratio-scale property, even after normalization, and precludes the occurrence of rank reversal under any condition. Our methodology includes the weighted geometric mean method for determining composite priority ratings as a special case.