Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces
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Bibliographic record
Abstract
In this paper, using improvement-valued maps, we define two types of E -Benson proper efficient elements for subsets within a linear space under a variable ordering map C .Consequently, we delve into studying two types of E -Benson proper efficient solutions of vector optimization problems under variable ordering structures.We establish relationships among different types of E -Benson proper efficient elements.Furthermore, we demonstrate that the two types of E -Benson proper efficiency, in relation to the ordering map C , not only unify and extend certain notions of (weakly) nondominated elements but also extend some well-known notions of Benson proper efficiency under fixed ordering structures.Lastly, under suitable assumptions, we establish linear scalarization theorems for E -Benson proper efficient solutions of vector optimization problems under variable ordering structures.Several examples are also provided to illustrate the derived results.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
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| Bibliometrics | 0.001 | 0.003 |
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| Open science | 0.000 | 0.000 |
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| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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