Optimal decisions under complex uncertainty - basic notions and a general algorithm for data-based decision making with partial prior knowledge described by interval probability. (English) Zbl 1056.62009

Augustin, Thomas

ZAMM, Z. Angew. Math. Mech. 84, No. 10-11, 678-687 (2004).

Summary: A powerful application of decision theory to engineering problems often has failed: The uncertainty underlying is too complex to be modelled adequately by a (precise) probability distribution. The present paper shows how recent generalizations of the usual calculus of probability can be utilized to deal powerfully with complex uncertainty in decision problems. Basic notions of the resulting theory of generalized expected loss and generalized risk are developed and discussed. In addition to this, also a general applicable algorithm is proposed to calculate optimal decision functions by linear programming.

MSC:

62C99	Statistical decision theory
62P30	Applications of statistics in engineering and industry; control charts
62A01	Foundations and philosophical topics in statistics
90C90	Applications of mathematical programming
90C05	Linear programming

Keywords:

decision making; risk; generalized risk; generalized expected loss; ambiguity; interval probability; imprecise probabilities; random sets; capacities; belief functions; Choquet integral; \(\Gamma\)-minimax principle; expert systems

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