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Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis

  • Qamrul Hasan AnsariEmail author
  • Elisabeth Köbis
  • Pradeep Kumar Sharma
Article

Abstract

In this paper, we characterize different kinds of multiobjective robustness concepts via the well-known oriented distance function. By using characterizations of several set relations via the oriented distance function, together with the help of image space analysis, we construct some suitable subsets of the scalarization image space to obtain equivalent characterizations for various robust solutions for uncertain multiobjective optimization problems based on a set approach.

Keywords

Oriented distance function Set relations Image space analysis Uncertain multiobjective optimization Robustness 

Mathematics Subject Classification

49J53 90C29 90C30 90C31 

Notes

Acknowledgements

Authors are grateful to the referees for their valuable suggestions and comments to improve the first draft of this paper. In this paper, Q. H. Ansari was supported by a research Grant of DST-SERB No. EMR/2016/005124.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  3. 3.Institute of MathematicsMartin-Luther-University Halle-WittenbergHalle (Saale)Germany

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