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.