<p>This article focuses on a robust fractional interval-valued programming problem with data uncertainty (RFP) and its associated robust <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1239_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {E}_{\mathbb {R}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">E</mi> <mi mathvariant="double-struck">R</mi> </msub> </math></EquationSource> </InlineEquation>- fractional interval-valued programming problem with data uncertainty (ERFP). We establish the robust parametric <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1239_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {E}_{\mathbb {R}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">E</mi> <mi mathvariant="double-struck">R</mi> </msub> </math></EquationSource> </InlineEquation>-Karush–Kuhn–Tucker optimality criteria for (ERFP) involving <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1239_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {E}_{\mathbb {R}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">E</mi> <mi mathvariant="double-struck">R</mi> </msub> </math></EquationSource> </InlineEquation>-convexity assumptions. Finally, the sufficient optimality criteria are validated by a numerical example.</p>

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Robust parametric \({\mathbb {E}_{\mathbb {R}}}\)-Karush–Kuhn–Tucker optimality criteria for fractional interval-valued optimization problems

  • Krishna Kummari,
  • Rekha R. Jaichander,
  • Savin Treanţă,
  • Cristina Florentina Pirje

摘要

This article focuses on a robust fractional interval-valued programming problem with data uncertainty (RFP) and its associated robust \({\mathbb {E}_{\mathbb {R}}}\) E R - fractional interval-valued programming problem with data uncertainty (ERFP). We establish the robust parametric \({\mathbb {E}_{\mathbb {R}}}\) E R -Karush–Kuhn–Tucker optimality criteria for (ERFP) involving \({\mathbb {E}_{\mathbb {R}}}\) E R -convexity assumptions. Finally, the sufficient optimality criteria are validated by a numerical example.