Aggregation of Partly Inconsistent Preference Information

Traditionally the preference information is expressed as a preference relation defined upon the power set of the set of the decision alternatives. The preference information required for the method described in this paper is significantly less complex and is simply defined on the decision set. For every decision goal the preference of the decision alternatives for this goal is defined upon the set of decision alternatives as a linear ranking of the decision alternatives. It is discussed in which way a decision making approach based on interactions between goals is applied using this kind of preference information even if it is partly inconsistent. In a recent work for the case of consistent preference information a link to the theory of matroids was found. In this paper the case of partly inconsistent preference information is considered and a new link to the theory of matroids is given.