Generalization of equitable efficiency in multiobjective optimization problems by the direct sum of matrices

We suggest an a priori method by introducing the concept of AP - equitable efficiency. The preferences matrix AP , which is based on the partition P of the index set of the objective functions, is given by the decision-maker. We state the certain conditions on the matrix AP that guarantee the preference relation ⪯eAP to satisfy the strict monotonicity and strict P -transfer principle axioms. A problem most frequently encountered in multiobjective optimization is that the set of Pareto optimal solutions provided by the optimization pro-cess is a large set. Hence, the decision-making based on selecting a unique preferred solution becomes difficult. Considering models with Ar P -equitable efficiency and A∞ P -equitable efficiency can help the decision-maker for over-coming this difficulty, by shrinking the solution set.