Generalized Edgeworth–Pareto principle

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.