Volume 5 • Issue 1 | March 2021

Decision making under interval uncertainty: toward (somewhat) more convincing justifications for Hurwicz optimism-pessimism approach

Warattaya Chinnakum, Laura Berrout Ramos, Olugbenga Iyiola, Vladik Kreinovich


Purpose – In real life, we only know the consequences of each possible action with some uncertainty. A typical example is interval uncertainty, when we only know the lower and upper bounds on the expected gain. A usual way to compare such interval-valued alternatives is to use the optimism–pessimism criterion developed by Nobelist Leo Hurwicz. In this approach, a weighted combination of the worst-case and the bestcase gains is maximized. There exist several justifications for this criterion; however, some of the assumptions behind these justifications are not 100% convincing. The purpose of this paper is to find a more convincing explanation.

Design/methodology/approach – The authors used utility approach to decision-making.

Findings – The authors proposed new, hopefully more convincing, justifications for Hurwicz’s approach.

Originality/value – This is a new, more intuitive explanation of Hurwicz’s approach to decision-making under interval uncertainty.


  1. Fishburn, P.C. (1969), Utility Theory for Decision Making, John Wiley and Sons, New York, NY.
  2. Hurwicz, L. (1951), “Optimality criteria for decision making under ignorance”, Cowles Commission Discussion Paper, Statistics, No. 370.
  3. Kreinovich, V. (2014), “Decision making under interval uncertainty (and beyond)”, in Guo, P. and Pedrycz, W. (Eds), Human-Centric Decision-Making Models for Social Sciences, Springer Verlag, pp. 163-193.
  4. Luce, R.D. and Raiffa, R. (1989), Games and Decisions: Introduction and Critical Survey, Dover, New York, NY.
  5. Nguyen, H.T., Kosheleva, O. and Kreinovich, V. (2009), “Decision making beyond arrow’s ‘impossibility theorem’, with the analysis of effects of collusion and mutual attraction”, International Journal of Intelligent Systems, Vol. 24 No. 1, pp. 27-47.
  6. Raiffa, H. (1997), Decision Analysis, McGraw-Hill, Columbus, OH.
  7. Further reading
  8. Kreinovich, V. (2017), “Decision making under interval (and more general) uncertainty: monetary vs utility approaches”, Journal of Computational Technologies, Vol. 22 No. 2, pp. 37-49.