How General Is Fuzzy Decision Making?

In many practical situations, users describe their preferences in imprecise (fuzzy) terms. In such situations, fuzzy techniques are a natural way to describe these preferences in precise terms. Of course, this description is only an approximation to the ideal decision making that a person would perform if we took time to elicit his/her exact preferences. How accurate is this approximation? When can fuzzy decision making -- potentially -- describe the exact decision making, and when there is a limit to the accuracy of fuzzy approximations? In this paper, we show that decision making can be precisely described in fuzzy terms if and only if different numerical characteristics describing the alternatives are independent -- in the sense that if for two alternatives, all but one characteristics have the same value, then the preference between these two alternatives depends only on the differing characteristic and does not depend on the values of all other characteristics