Multi-Goal Aggregation of Reduced Preference Relations Based on Fuzzy Interactions between Decision Goals

Many aggregation operators like fuzzy integrals and similar require a preference relation as input. If the number of decision alternatives increases it becomes almost impossible to provide the exponentially increasing number of preference statements which are needed because a preference relation is defined upon the power set of the set of decision alternatives. If, as in many real world applications, the number of decision goals increases, it is also almost impossible to supervise the consistency of preference statements with respect to the interactions between the decision goals. In this paper it is discussed in which way a decision making approach based on interactions between goals is applied in order to use preference information that is not defined upon the power set of the set decision alternatives but simply on the decision set itself. Instead of defining the preferences upon the power set of the decision alternatives with respect to all the goals, for every decision goal the preference of the decision alternatives for this goal is defined upon the set of decision alternatives by a linear preference ranking of the decision alternatives. Consequences for both decision modeling based on classical preference relations and based on weighted sums are discussed. Keywords– Aggregation complexity, decision making, interactions between goals, reduced preference relation, weighted sum.