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Decision Theory With Imprecise Probabilities

Author

Listed:
  • R. A. ALIEV

    (Azerbaijan State Oil Academy, Baku, Azerbaijan Azadlig ave. 20, AZ1010, Azerbaijan)

  • W. PEDRYCZ

    (Department of Electrical & Computer Engineering, University of Alberta, Edmonton AB T6R 2G7, Canada;
    System Research Institute, Polish Academy of Sciences, Warsaw, Poland)

  • O. H. HUSEYNOV

    (Azerbaijan State Oil Academy, Baku, Azerbaijan Azadlig ave. 20, AZ1010, Azerbaijan)

Abstract

There is an extensive literature on decision making under uncertainty. Unfortunately, up to date there are no valid decision principles. Experimental evidence has repeatedly shown that widely used principle of maximization of expected utility has serious shortcomings. Utility function and nonadditive measures used in nonexpected utility models are mainly considered as real-valued functions whereas in reality decision-relevant information is imprecise and therefore is described in natural language. This applies, in particular, to imprecise probabilities expressed by terms such as likely, unlikely, probable, etc. The principal objective of the paper is the development of computationally effective methods of decision making with imprecise probabilities. We present representation theorems for a nonexpected fuzzy utility function under imprecise probabilities. We develop an effective decision theory when the environment of fuzzy events, fuzzy states, fuzzy relations and fuzzy constraints are characterized by imprecise probabilities. The suggested methodology is applied for a real-life decision-making problem.

Suggested Citation

  • R. A. Aliev & W. Pedrycz & O. H. Huseynov, 2012. "Decision Theory With Imprecise Probabilities," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 271-306.
    • Handle: RePEc:wsi:ijitdm:v:11:y:2012:i:02:n:s0219622012400032
    DOI: 10.1142/S0219622012400032
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    References listed on IDEAS

    as
    1. Meglena Jeleva, 2000. "Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 25(1), pages 7-28, June.
    2. George A. Akerlof, 2009. "How Human Psychology Drives the Economy and Why It Matters," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(5), pages 1175-1175.
    3. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, January.
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