A new framework for the Bayesian analysis of single-stage decision problems with imprecise utilities

• Published in: Fuzzy sets and systems Vol. 159; no. 24; pp. 3271 - 3280
• Main Authors: Rodríguez-Muñiz, Luis J., López-Díaz, Miguel
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.12.2008; Elsevier
• Subjects: Applied sciences; Bayesian analysis of single-stage decision problems; Circuit properties; Computer science; control theory; systems; Control theory. Systems; Decision analysis; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Information, signal and communications theory; Iterated expectation; Mathematical methods; Miscellaneous; Random upper semicontinuous function; System theory; Telecommunications and information theory; Theoretical computing; Uncertainty modelling; Decision analysis; Random upper semicontinuous function; Uncertainty modelling; Bayesian analysis of single-stage decision problems; Iterated expectation; Engineering; Fuzzy system; Semicontinuous function; Normal form; Information processing; Fuzzy set; Mathematical model
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2008.05.010

A mathematical framework to model the Bayesian analysis of single-stage decision problems with imprecise utilities is proposed. The main advantage of this model with respect to previous models for such a problem, is that product measurability of the utility function is not necessary, since this model involves iterated expectations instead of an integral over a product space. Conditions for the equivalence between the extensive and normal forms of the Bayesian analysis, within the proposed framework, are obtained. The model is illustrated with an example in which the utility function is not product measurable.