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

Iranian Journal of Numerical Analysis and Optimization

مقاله 17، دوره 13، شماره 1 - شماره پیاپی 24، خرداد 2023، صفحه 80-101   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.69731.1023

نویسندگان

F. Ahmadi؛ A. R. Salajegheh؛ D. Foroutannia^*

Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

چکیده

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.

کلیدواژه‌ها

Nondominated؛ equitable efficiency؛ AP -equitable efficiency؛ Multiobjective programming

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