Skip to main content
SpringerLink
Log in

On the relation of the notions of potential optimality and non-dominance

  • Notes, Chronicles, Information
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We study the interrelationship between the notions of potential optimality and nondominance without the assumption of the existence of value functions monotonic with respect to a non-strict preference.

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. Xu, Z., A Survey of Preference Relations, Int. J. Gen. Syst., 2007, vol. 36, pp. 179–203.

    Article  MATH  MathSciNet  Google Scholar 

  2. Podinovskii, V.V., Vvedenie v teoriyu vazhnosti kriteriev v mnogokriterial’nykh zadachakh prinyatiya reshenii (Introduction to Criteria Importance Theory in Multicriterial Decision Making Problems), Moscow: Fizmatlit, 2007.

    Google Scholar 

  3. Hazen, G.B., Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory, Oper. Res., 1986, vol. 34, pp. 296–310.

    Article  MATH  MathSciNet  Google Scholar 

  4. Athanassopoulos, A.D. and Podinovski, Vic.V., Dominance and Potential Optimality inMultiple Criteria Decision Analysis with Imprecise Information, J. Oper. Res. Soc., 1997, vol. 48, pp. 142–150.

    MATH  Google Scholar 

  5. Eum, E.S., Park, K.S., and Kim, S.H., Establishing Dominance and Potential Optimality in Multi-Criteria Decision Analysis with Imprecise Weight and Value, Comp. Oper. Res., 2001, vol. 28, pp. 397–409.

    Article  MATH  Google Scholar 

  6. Mateos, A., Rios-Insua, S., and Jimenes, A., Dominance, Potential Optimality and Alternative Ranking in Imprecise Multi-Attribute Decision Making, J. Oper. Res. Soc., 2007, vol. 58, pp. 326–336.

    Article  MATH  Google Scholar 

  7. White, D.J., Notes in Decision Theory: Optimality and Efficiency. II, Eur. J. Oper. Res., 1980, vol. 4, pp. 426–427.

    Article  MATH  Google Scholar 

  8. White, D.J., Optimality and Efficiency, New York: Wiley, 1982.

    MATH  Google Scholar 

  9. Sen, A.K., Collective Choice and Social Welfare, San Francisco: Holden Day, 1970.

    MATH  Google Scholar 

  10. Ozernoi, V.M. and Gaft, M.G., The Methodology of Solving Discrete Multicriterial Problems, in Mnogokriterial’nye zadachi prinyatiya reshenii (Multicriterial Decision Making Problems), Gvishiani, D.M. and Emel’yanov, S.V., Eds., Moscow: Mashinostroenie, 1978, pp. 14–47.

    Google Scholar 

  11. Szpilrajn, E., Sur l’extension de l’ordre partiel, Fundamenta Mathematicae, 1930, vol. 16, pp. 386–389.

    MATH  Google Scholar 

  12. Podinovskii, V.V., The Guaranteed Result Principle for Partial Preference Relations, Zh. Vychisl. Mat. Mat. Fiz., 1979, no. 6, pp. 1436–1450.

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

    Article  MATH  Google Scholar 

  14. Podinovskii, V.V., Optimality and Non-Dominance, Modern problems of informatization in the analysis and synthesis of technological and software systems, Proc. XVI Intern. Open Sci. Conf., Voronezh: Nauchnaya Kniga, 2011, vol. 16, pp. 332–334.

    Google Scholar 

  15. Mal’tsev, A.I., Algebraicheskie sistemy (Algebraic Systems), Moscow: Nauka, 1970.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    V. V. Podinovskii

Authors
  1. V. V. Podinovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.V. Podinovskii, 2012, published in Avtomatika i Telemekhanika, 2012, No. 1, pp. 184–187.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Podinovskii, V.V. On the relation of the notions of potential optimality and non-dominance. Autom Remote Control 73, 167–170 (2012). https://doi.org/10.1134/S0005117912010146

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912010146

Keywords

Search

Navigation