On the Difference Between the Cardinalities of Measurable Value Functions and Von Neumann-Morgenstern Utility Functions | Zendy

Jean M. Deichtmann | Zendy; François Sainfort | Zendy

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On the Difference Between the Cardinalities of Measurable Value Functions and Von Neumann-Morgenstern Utility Functions

Author(s) -

Jean M. Deichtmann,

François Sainfort

Publication year - 1997

Publication title -

operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.797

H-Index - 140

eISSN - 1526-5463

pISSN - 0030-364X

DOI - 10.1287/opre.45.2.307

Subject(s) - von neumann architecture , cardinality (data modeling) , multiplicative function , mathematics , generalization , value (mathematics) , mathematical economics , measurable function , decomposition , decomposition theorem , von neumann–morgenstern utility theorem , discrete mathematics , pure mathematics , expected utility hypothesis , computer science , mathematical analysis , statistics , ecology , biology , bounded function , data mining

Dyer and Sarin Dyer, J. S., R. K. Sarin. 1979. Measurable multiattribute value functions. Opns. Res.27 810-822. proposed an important generalization of the additive-multiplicative decomposition theorem for von Neumann-Morgenstern vNM utility functions to measurable value functions based on the cardinality property of measurable value functions. However, because of a difference between the cardinality of measurable value functions and the cardinality of vNM utility functions, an additional technical condition is needed, and presented here, for the decomposition theorem to hold.

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