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This paper presents a theory of measurable multiattribute value functions. Measurable value functions are based on the concept of a “preference difference” between alternatives and provide an interval scale of measurement for preferences under certainty. We present conditions for additive, multiplicative, and more complex forms of the measurable multiattribute value function. This development provides a link between the additive value function and multiattribute utility theory.
Dyer et al. (1979) studied this question.