Generalized Edgeworth-Pareto principle

摘要

The general multicriteria choice problem with m individual preference relations and an asymmetric collective preference relation is considered. The concept of a k-effective alternative is introduced, which coincides with an effective alternative for k = 1 and represents a weakly effective alternative for k = m. For the other integer values of k, it lies somewhere in between. In terms of the general multicriteria choice problem, the Pareto axiom and the exclusion axiom for dominated alternatives are stated. Assuming that these axioms hold, a generalized Edgeworth-Pareto principle is established, which was earlier introduced by the author in the special case k = 1. The results are extended to a fuzzy collective preference relation and to a fuzzy set of initial alternatives.