two techniques to reduce the pareto optimal solutions in multiobjective optimization problems

In this study, for a decomposed multi-objective optimization problem, we  propose the direct sum of the preference matrices of the  subproblems provided by the decision maker (dm). then, using this matrix, we present a new generalization of the rational efficiency concept for solving the multi-objective optimization problem (mop). a problem that sometimes occurs in multi-objective optimization is the existence of a large set of pareto optimal solutions. hence, decision making based on selecting a unique preferred solution becomes difficult. considering models with the concept of generalized rational efficiency can relieve some of the burden from the dm by shrinking the solution set. this paper discusses both theoretical and practical aspects of rationally efficient solutions related to this concept. moreover, we present two techniques to reduce the pareto optimal solutions using. the first technique involves using the powers of the preference matrix, while the second technique involves creating a new preference matrix by modifying the decomposition of the mop.