Generalized equitable preference in multiobjective programming

The concept of equitability in multiobjective programming is generalized within a framework of convex cones. Two models are presented. First, more general polyhedral cones are assumed to determine the equitable preference. Second, the Pareto cone appearing in the monotonicity axiom of equitability is replaced with a permutation-invariant polyhedral cone. The conditions under which the new models are related and satisfy original and modified axioms of the equitable preference are developed. Relationships between generalized equitability and relative importance of criteria and stochastic dominance are revealed.