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Optimal decisions under complex uncertainty – basic notions and a general algorithm for data‐based decision making with partial prior knowledge described by interval probability
Author(s) -
Augustin Th.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410151
Subject(s) - interval (graph theory) , computer science , probability distribution , applied probability , mathematics , mathematical optimization , probability theory , calculus (dental) , algorithm , statistics , medicine , dentistry , combinatorics
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.