Theory and Decision

, Volume 49, Issue 2, pp 127–150 | Cite as

Decision Making in `Random in a Broad Sense' Environments

  • V.I. Ivanenko
  • B. Munier
Article

Abstract

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.

Uncertainty Random in a broad sense phenomena Statistical regularity Principle of guaranteed result Optimality criterion choice 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Bell D., Raiffa H. & Tversky A. (eds) (1991), Decision Making (Cambridge, Mass.: Cambridge University Press).Google Scholar
  2. Borel, E. (1961), Probabilité et certitude, 3rd ed. (1st ed.: 1950) (Paris: P.U.F.).Google Scholar
  3. Cramer H. (1958), Mathematical Methods of Statistics (Princeton: Princeton Univ. Press).Google Scholar
  4. Dacunha-Castelle, D. (1996), Chemins de l'aléatoire (Paris: Flammarion).Google Scholar
  5. Edwards, R.E. (1965), Functional Analysis, Theory and Applications (New York: Holt, Rinehart & Winston).Google Scholar
  6. Ivanenko V.I. & Labkovsky, V.A. (1990), The Uncertainty Problem in Decision Making, Naukova Dumka, Kiev (book in Russian).Google Scholar
  7. Ivanenko, V.I. & Labkovsky, V.A. (1986), On the functional dependence between the available information and the chosen optimality principle, in Stochastic Optimization, Lecture Notes in Control and Information Sciences, Springer-Verlag, 388–392.Google Scholar
  8. Ivanenko, V.I. & Zorych, I.V. (1997),On the G(l)-independence of two sequences and their joint statistical regularity, Kibernetika i sistemnyij analiz, Nr. 2, Kiev, 91–99 (in Russian).Google Scholar
  9. Ivanenko, V.I., Munier, B. & Zorych, I.V. (1997), On the construction of the regularity of statistically unstable sequences, Problemy upravleniya i informatiki, Nr. 4, Kiev, 119–122 (in Russian).Google Scholar
  10. Kelley, J.L. (1957), General Topology (Princeton, N.J.: D. Van Nostrand Company).Google Scholar
  11. Knight, F.H. (1921), Risk, Uncertainty and Profit (Boston: Houghton Mifflin).Google Scholar
  12. Kolmogorov, A.N. (1991), On a Logical Foundation of Probability Theory, Algorithm, Information, Complexity, Mathematics and Cybernetics 1: 42–44.Google Scholar
  13. Luce, R.D. & Raiffa, H. (1957), Games and Decisions (New York: Wiley).Google Scholar
  14. Munier, B.R. (1991), Market Uncertainty and the Process of Belief Formation, Journal of Risk and Uncertainty 4: 233–250.Google Scholar
  15. Munier, B.R. (1995), Complexity and Strategic Decision under Uncertainty: How Can we Adapt the Theory?, in B.R. Munier (ed.), Markets, Risk and Money (Dordrecht/Boston: Kluwer Academic Publishers).Google Scholar
  16. Vilkas, E.J. (1979), Axiomatic Approach to Optimality Principles, in Modern State of Operations Research, Moskva, 101–115 (in Russian).Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • V.I. Ivanenko
    • 1
    • 2
  • B. Munier
    • 1
    • 2
  1. 1.Kiev Polytechnic InstituteKievUkraine
  2. 2.Ecole Normale SupérieureCachanFrance

Personalised recommendations