Decision Analysis under Partial Information

  • Vladislav V. Podinovski
  • Victor V. Podinovski
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 465)


The use of partial (incomplete) qualitative data in multiple criteria decision making problems under uncertainty is considered. It is assumed that the preferences of a decision maker (DM) between certain consequences and the probabilities of the uncertain factor values are given in the form of binary relations. The following three main issues are addressed. First, the DM’s preference relation for uncertain consequences is deduced from the available information. Secondly, we discuss how this, normally partial, preference relation can be further extended given the information about the DM’s attitude towards risk. Thirdly, we show how the available qualitative information can be used in conjunction with the maxmin optimality principle.


Multiple criteria uncertainty qualitative probability preference relations lexicographic maxmin 


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  1. 1.
    Naumov, G. Ye., Podinovski, V.V., and Podinovski, Vic.V. (1993) Subjective Probability: Representation and Derivation Methods. Journal of Computer and System Sciences International, 31, 12 – 23.Google Scholar
  2. 2.
    Kraft, C.H., Pratt, J.W., and Seidenberg, A. (1959) Intuitive probability on finite sets. Annals of Mathematical Statistics, 30, 408 – 419.CrossRefGoogle Scholar
  3. 3.
    Fishburn, P.C. (1964) Decision and Value Theory, New York, John Wiley and Sons.Google Scholar
  4. 4.
    Athanassopoulos, A.D., and Podinovski, Vic.V. Dominance and Potential Optimality in Multiple Criteria Decision Analysis with Imprecise Information, (forthcoming inJournal of Operational Research Society).Google Scholar
  5. 5.
    Whitmore, G.A., and Findlay, M.C., eds. (1978) Stochastic Dominance, Lexington, Mass., D.C. Heath.Google Scholar
  6. 6.
    Podinovski, V.V. (1978) On Relative Importance of Criteria in Multiobjective Decision Making Problems. In: Multiobjective Decision Problems, Moscow, Mashinostroenie Publishing House, 48 – 92. (in Russian)Google Scholar
  7. 7.
    Podinovski, V.V. (1979) An Axiomatic Solution of the Problem of Criteria Importance in Multicriterial Problems. In:Operations Research Theory: State of the Art, Moscow, Nauka Publishing House, 117 – 149. (in Russian)Google Scholar
  8. 8.
    Podinovski, V.V. (1994) Criteria Importance Theory. Mathematical Social Sciences, 27, 237 – 252.CrossRefGoogle Scholar
  9. 9.
    Podinovski, V.V. (1993) Problems with Importance-Ordered Criteria. In: J. Wessels and A.P. Wierzbicki, eds., User-Oriented Methodology and Techniques of Decision Analysis and Support, Berlin, Springer Verlag, 150 – 155.CrossRefGoogle Scholar
  10. 10.
    Osipova, V.A., Podinovski, V.V., and Yashina, N.P. (1984) On Non- contradictory Extension of Preference Relations in Decision Making Problems. USSR Computational Mathematics and Mathematical Physics, 24, 128 – 134.CrossRefGoogle Scholar
  11. 11.
    Podinovski, V.V. (1976) Multicriterial Problems with Importance-Ordered Criteria. Automation and Remote Control, 37, 1728 – 1736.Google Scholar
  12. 12.
    Podinovski, V.V. (1978) Importance Coefficients of Criteria in Decision-Making Problems. Automation and Remote Control, 39, 1514 – 1524.Google Scholar
  13. 13.
    Podinovski, V.V. (1975) Multicriterial Problems with Uniform Equivalent Criteria, USSR Computational Mathematics and Mathematical Physics, 15, 47 – 60.CrossRefGoogle Scholar
  14. 14.
    Keeney, R.L., and Raiffa, H. (1976) Decisions with Multiple Objectives, New York, John Wiley and Sons.Google Scholar
  15. 15.
    Podinovski, Vic.V. (1983) Criterion of Probabilistic-Lexicographic Maximin. Moscow University Computational Mathematics and Cybernetics, 39 – 45.Google Scholar
  16. 16.
    Podinovski, Vic.V. (1993) Extension of Partial Binary Relations in Decision-Making Models. Computational Mathematics and Modeling. 4, 263 – 264.CrossRefGoogle Scholar
  17. 17.
    Podinovski, Vic.V. (1985) A Lexicographic Approach to Decision Making under Uncertainty. In: The Software of Computing Systems. Moscow, Moscow University Press, 104 – 119. (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Vladislav V. Podinovski
    • 1
  • Victor V. Podinovski
    • 2
  1. 1.Academy of Labour and Social RelationsMoscowRussia
  2. 2.Warwick Business School, University of WarwickCoventryUK

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