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Decision making with interval probabilities

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  • Guo, Peijun
  • Tanaka, Hideo

Abstract

Handling uncertainty by interval probabilities is recently receiving considerable attention by researchers. Interval probabilities are used when it is difficult to characterize the uncertainty by point-valued probabilities due to partially known information. Most of researches related to interval probabilities, such as combination, marginalization, condition, Bayesian inferences and decision, assume that interval probabilities are known. How to elicit interval probabilities from subjective judgment is a basic and important problem for the applications of interval probability theory and till now a computational challenge. In this work, the models for estimating and combining interval probabilities are proposed as linear and quadratic programming problems, which can be easily solved. The concepts including interval probabilities, interval entropy, interval expectation, interval variance, interval moment, and the decision criteria with interval probabilities are addressed. A numerical example of newsvendor problem is employed to illustrate our approach. The analysis results show that the proposed methods provide a novel and effective alternative for decision making when point-valued subjective probabilities are inapplicable due to partially known information.

Suggested Citation

  • Guo, Peijun & Tanaka, Hideo, 2010. "Decision making with interval probabilities," European Journal of Operational Research, Elsevier, vol. 203(2), pages 444-454, June.
  • Handle: RePEc:eee:ejores:v:203:y:2010:i:2:p:444-454
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    Cited by:

    1. Ahn, Byeong Seok & Park, Haechurl, 2014. "Establishing dominance between strategies with interval judgments of state probabilities," Omega, Elsevier, vol. 49(C), pages 53-59.
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    3. Li, Kevin W. & Wang, Zhou-Jing & Tong, Xiayu, 2016. "Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices," European Journal of Operational Research, Elsevier, vol. 250(2), pages 628-638.
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    8. Chun-xiang Guo & Ying Peng, 2015. "Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory," Group Decision and Negotiation, Springer, vol. 24(5), pages 753-775, September.
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