Preference Function Modelling: The Mathematical Foundations of Decision Theory

We establish the conditions that must be satisfied for the mathematical operations of linear algebra and calculus to be applicable. The mathematical foundations of decision theory and related theories depend on these conditions which have not been correctly identified in the classical literature. Operations Research and Decision Analysis Societies should act to correct fundamental errors in the mathematical foundations of measurement theory, utility theory, game theory, mathematical economics, decision theory, mathematical psychology, and related disciplines.

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