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Volume 5 • Issue 1 | March 2021

Decision-making under interval uncertainty revisited

Olga Kosheleva, Vladik Kreinovic, Uyen Pham

06/04/2021 130 0 0
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Decision-making Invariance Interval uncertainty Additivity

Abstract:

Purpose – In many real-life situations, we do not know the exact values of the expected gain corresponding to different possible actions, we only have lower and upper bounds on these gains – i.e., in effect, intervals of possible gain values. The purpose of this study is to describe all possible ways to make decisions under such interval uncertainty.

Design/methodology/approach – The authors used both natural invariance and additivity requirements.

Findings – The authors demonstrated that natural requirements – invariance or additivity – led to a two-parametric family of possible decision-making strategies.

Originality/value – This is a first description of all reasonable strategies for decision-making under interval uncertainty – strategies that satisfy natural requirements of invariance or additivity.

References:

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  2. Hurwicz, L. (1951), “Optimality criteria for decision making under ignorance”, Cowles commission discussion paper, Statistics, Vol. 1951 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. Stefanini, L., Sorini, L. and Amicizia, B. (2019a), “Interval analysis and calculus for interval-valued functions of a single variable. Part I: partial orders, gH derivative, monotonicity”, Axioms, Vol. 8 No. 4, p. 113.
  8. Stefanini, L., Sorini, L. and Amicizia, B. (2019b), “Interval analysis and calculus for interval-valued functions of a single variable. Part II: extremal points, convexity, periodicity”, Axioms, Vol. 8 No. 4, p. 114.

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