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 prefere...

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Published in:Iranian journal of numerical analysis and optimization Vol. 13; no. 1; pp. 80 - 101
Main Authors: F. Ahmadi, A. R. Salajegheh, D. Foroutannia
Format: Journal Article
Language:English
Published: Ferdowsi University of Mashhad 01.03.2023
Subjects:
ap -equitable efficiency
equitable efficiency
multiobjective programming
nondominated
ISSN:2423-6977, 2423-6969
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Abstract 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.
AbstractList 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.
Author D. Foroutannia
F. Ahmadi
A. R. Salajegheh
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  organization: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
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Snippet 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...
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SubjectTerms ap -equitable efficiency
equitable efficiency
multiobjective programming
nondominated
Title Generalization of equitable efficiency in multiobjective optimization problems by the direct sum of matrices
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