Skip to main content
SpringerLink
Log in

Analysis of the Sensitivity of Solutions of Multi-Criteria Problems Based on Parametric Partial Preference Relations

  • Optimization, System Analysis, and Operations Research
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We give a survey of approaches for analyzing the sensitivity of non-dominated alternatives to changes in the parameters of partial quasi-orderings that define preferences. Such parameters can include values of importance coefficients for different criteria or boundaries of interval estimates of the degrees of superiority in the importance of some criteria over others, boundaries of intervals of criteria value tradeoffs uncertainty and others.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Impact assessment guidelines. http://ec.europa.eu/smart-regulation/impact/commission_guidelines/docs/iag_2009_en.pdf

  2. Handbook of Sensitivity Analysis, Saltelli, A., Chan, K., and Scott, M., Eds., New York: Wiley, 2009.

  3. Ashmanov, S.A., Lineinoe programmirovanie (Linear Programming), Moscow: Fizmatlit, 1981.

    Google Scholar 

  4. Gal, T. and Greenberg, H.J., Advances in Sensitivity Analysis and Parametric Programming, New York: Kluwer, 1997.

    Book  MATH  Google Scholar 

  5. Rios-Insua, D. and French, S., A Framework for Sensitivity Analysis in Discrete Multi-Objective Decision-Making, Eur. J. Oper. Res., 1991, vol. 54, pp. 176–190.

    Article  MATH  Google Scholar 

  6. Wolters, W.T.M. and Mareschal, B., Novel Types of Sensitivity Analysis for Additive MCDM Methods, Eur. J. Oper. Res., 1995, vol. 81, pp. 281–290.

    Article  MATH  Google Scholar 

  7. French, S., Mathematical Programming Approaches to Sensitivity Calculations in Decision Analysis, J. Oper. Res. Soc, 1992, vol. 43, pp. 813–819.

    Article  MATH  Google Scholar 

  8. Triantaphyllou, E. and Sanchez, A., A Sensitivity Analysis Approach for Some Deterministic Multi-Criteria Decision Making Methods, Decision Sci., 1997, vol. 28, pp. 151–194.

    Article  Google Scholar 

  9. Erkut, E. and Tarimcilar, M., On Sensitivity Analysis in the Analytic Hierarchy Process, IMA J. Manage. Math., 1991, vol. 3, pp. 61–83.

    Article  MathSciNet  MATH  Google Scholar 

  10. Triantaphyllou, E., Sensitivity Analysis Approach for MCDM Methods, Ch. 8, Multi-Criteria Decision Making Method: A Comparative Study, New York: Kluver, 2000.

    Book  MATH  Google Scholar 

  11. Huang, Y.-F., Enhancement on Sensitivity Analysis of Priority in Analytic Hierarchy Process, Int. J. General Syst., 2002, vol. 31, pp. 531–542.

    Article  MathSciNet  MATH  Google Scholar 

  12. Delgado, M.G. and Sendra, J.B., Sensitivity Analysis in Multicriteria Spatial Decision-Making: A Review, Human Ecologic. Risk Assesment, 2004, vol. 10, pp. 1173–1187.

    Article  Google Scholar 

  13. May, J.H., Shang, J., Tjader, Y.C., and Vargas, L.G., A New Methodology for Sensitivity and Stability Analysis of Analytic Network Models, Eur. J. Oper. Res., 2013, vol. 224, pp. 180–188.

    Article  MathSciNet  MATH  Google Scholar 

  14. Genc, T., Sensitivity Analysis on PROMETHEE and TOPSIS Weights, Int. J. Manage. Decision Making, 2014, vol. 13, pp. 403–421.

    Article  Google Scholar 

  15. Doan, N.A.V. and De Smet, Y., An Alternative Weight Sensitivity Analysis for PROMETHEE II Rankings, Omega, 2018, vol. 80, pp. 166–174.

    Article  Google Scholar 

  16. Vetschera, R., Sensitivity Analysis for the ELECTRE Multicriteria Method, Zeitschrift Oper. Res., 1986, vol. 30, no. 4, pp. B99–B117.

    MATH  Google Scholar 

  17. Tervonen, T., Figueira, J.R., Lahdelma, R., and Salminen, P., SMAA-III. A Simulation-Based Approach for Sensitivity Analysis of ELECTRE III, in Real-Time and Deliberative Decision Making: Application to Emerging Stressors, Linkov, I., Ferguson, E., and Magar, V.S., Eds., New York: Springer, 2008, pp. 241–253.

    Google Scholar 

  18. Pamucar, D.S., Bozanic, D., and Randelovic, A., Multi-Criteria Decision Making: An Example of Sensitivity Analysis, Serb. J. Manage., 2017, vol. 12, no. 1, pp. 1–27.

    Article  Google Scholar 

  19. Sitarz, S., Approaches to Sensitivity Analysis in MOLP, Int. J. Inform. Technol. Comput. Sci, 2014, no. 03, pp. 54–60.

    Article  Google Scholar 

  20. Podinovski, V.V., Analyzing the Stability of Choice for the Partial Preference Relation, Sci. Tech. Inf. Process., 2011, vol. 38, pp. 377–383.

    Article  Google Scholar 

  21. Podinovski, V.V., Sensitivity Analysis for Choice Problems with Partial Preference Relations, Eur. J. Oper. Res., 2012, vol. 221, pp. 198–204.

    Article  MathSciNet  MATH  Google Scholar 

  22. Podinovski, V.V., Vvedenie v teoriyu vazhnosti kriteriev v mnogokriterial’nykh zadachakh prinyatiya reshenii (Introduction to the Criteria Importance Theory in Multi-Criteria Decision Making Problems), Moscow: Fizmatlit, 2007.

    Google Scholar 

  23. Podinovskii, V.V. and Potapov, M.A., Criteria Importance in Multi-Criteria Decision Making Problems: Theory, Methods, Software, and Applications, Otkrytoe Obrazovan., 2012, no. 2, pp. 55–61.

    Google Scholar 

  24. Podinovski, V.V., On Relative Importance of Criteria in Multi-Criteria Decision Making Problems, in Mnogokriterial’nye zadachi prinyatiya reshenii (Multi-Criteria Decision Making Problems), Emel’yanov, S.V., Ed., Moscow: Mashinostroenie, 1978, pp. 48–82.

    Google Scholar 

  25. Podinovski, V.V., Parametric Importance of Criteria and Intervals of Value Tradeoffs Uncertainty in the Analysis of Multicriteria Problems, Comput. Math. Math. Phys., 2008, vol. 48, pp. 1981–1998.

    Article  MathSciNet  Google Scholar 

  26. Nelyubin, A.P., Stability Analysis for Multi-Criteria Choice with Methods of Criteria Importance Theory under Changes in Interval Importance Estimates, Otkrytoe Obrazovan., 2012, no. 2, pp. 47–51.

    Google Scholar 

  27. Nelyubin, A.P., Criteria Importance Theory: Sensitivity Analysis of Multicriterial Choice Using Interval Importance Information, Am. J. Control Syst. Inform. Technol, 2013, no. 1, pp. 13–17.

    Google Scholar 

  28. Podinovskii, V.V., Quantitative Importance of Criteria, Autom. Remote Control, 2000, vol. 61, no. 5, pp. 817–828.

    MathSciNet  Google Scholar 

  29. Podinovski, V.V., The Quantitative Importance of Criteria for MCDA, J. Multi-Criteria Decision Anal., 2002, vol. 11, pp. 1–15.

    Article  Google Scholar 

  30. Charnes, A. and Cooper, W.W., Management Models and Industrial Applications of Linear Programming, New York: Wiley, 1961.

    MATH  Google Scholar 

  31. Podinovski, V.V., Sensitivity of Multi-Criterial Selection to Change Assessment Assessments of Inho-mogeneous Criteria, Inform. Tekhnol. Nauk., Obrazovan. Upravlen., 2017, no. 4, pp. 23–27.

    Google Scholar 

  32. Podinovski, V.V., Sensitivity Analysis of Mulcriteria Choice to Changes in Intervals of Value Tradeoffs, Comput. Math. Math. Phys., 2018, vol. 58, pp. 461–469.

    Article  MathSciNet  MATH  Google Scholar 

  33. Men’shikova, O.R. and Podinovskii, V.V., Construction of the Preference Relation and the Core in Multicriterial Problems with Inhomogeneous Criteria that are Ordered with Respect to Importance, Comput. Math. Math. Phys., 1988, vol. 28, pp. 15–22.

    Article  MathSciNet  Google Scholar 

  34. Passy, U. and Levanon, Y., Analysis of Multi-Objective Decision Problems by the Indifference Band Approach, J. Optim. Theory Appl, 1984, vol. 43, pp. 205–235.

    Article  MathSciNet  MATH  Google Scholar 

  35. Podinovskii, V.V., Multi-Criteria Problems with Uniform Equally Valued Criteria, Zh. Vychisl. Mat. Mat. Fiz., 1975, no. 2, pp. 330–344.

    MathSciNet  MATH  Google Scholar 

  36. Podinovski, V.V., Potapov, M.A., Nelyubin, A.P., et al., A System for Choosing and Analyzing Multi-Criteria Solutions with Incomplete Preferences, Inform. Tekhnol. Nauk., Obrazovan. Upravlen., 2017, no. 2, pp. 50–57.

    Google Scholar 

Download references

Acknowledgments

This research was conducted with state support of the leading universities of the Russian Federation “5-100” and the State Research Program of the Institute of Computer-Aided Design of the RAS. The authors are grateful to the referee for useful comments that have helped improve the presentation of this work.

Author information

Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. V. Podinovski

  2. Institute of Computer-Aided Design, Russian Academy of Sciences, Moscow, Russia

    M. A. Potapov

Authors
  1. V. V. Podinovski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Potapov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. V. Podinovski or M. A. Potapov.

Additional information

This paper was recommended for publication by E.Ya. Rubinovich, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Podinovski, V.V., Potapov, M.A. Analysis of the Sensitivity of Solutions of Multi-Criteria Problems Based on Parametric Partial Preference Relations. Autom Remote Control 80, 1294–1303 (2019). https://doi.org/10.1134/S0005117919070075

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117919070075

Keywords

Search

Navigation