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Gil, María Angeles; López-Díaz, Miguel

Fundamentals and Bayesian analyses of decision problems with fuzzy-valued utilities. (English) Zbl 0949.91504

Int. J. Approx. Reasoning 15, No. 3, 203-224 (1996).
Summary: A manageable model to deal with general single-stage statistical decision problems with fuzzy-valued consequences is presented. The model is based on the notion of fuzzy random variable, as defined by M. L. Puri and D. Ralescu [J. Math. Anal. Appl. 114, 409-422 (1986; Zbl 0592.60004)], and also on a crisp ranking method for fuzzy numbers introduced by L. M. Campos and A. González [Fuzzy Sets Syst. 29, 145-153 (1989; Zbl 0672.90001)]. Fundamentals of the fuzzy utility function representing the preference pattern of the decision maker are established to guarantee the existence of this function by means of an axiomatic development. Bayesian analyses of these statistical decision problems in normal and extensive forms are formalized, and conditions for the equivalence of these analyses are given. Finally, an example illustrating the Bayesian analysis is considered.

Cited in 19 Documents

MSC:

91B06 Decision theory
03E72 Theory of fuzzy sets, etc.

Keywords:

single-stage statistical decision; fuzzy-valued consequences; fuzzy random variable; crisp ranking method; fuzzy utility function; Bayesian analysis

Citations:

Zbl 0592.60004; Zbl 0672.90001
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Full Text: DOI

References:

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