simultaneous use of two concepts of equitable efficiency and efficiency in solving multi-objective optimization problems

The two requirements of impartiality and equitability expressed with the principle of transfers are fulfilled by all objective functions in equitable multi-objective optimization. however, in some practical situations, the decision-maker believes these requirements should only be satisfied by a subset of objective functions. to solve the problem in this paper, we first divide the set of objective functions into two subsets, the subset given by the decision maker and its complement. then, we apply the concepts of equitable efficiency and efficiency for these two subsets, respectively. furthermore, we apply the mean and inequality measures for these subsets of objective functions and present the new mean-equity models for solving the location problem. we investigate the relationship between 2-efficient solutions of the new mean-equity models and efficient solutions of the location problem.