Fuzzy sets, probability and measurement

In recent years, the problem of uncertainty modeling has received much attention from scholars in artificial intelligence and decision theory. Various formal settings, including but not restricted to fuzzy sets and possibility measures, have been proposed, based on different intuitions, and dealing with various kinds of uncertain data. The two main research directions are upper and lower probabilities which convey the idea of imprecisely estimated probability measures, and distorted probabilities for the descriptive assessment of partial belief. Possibility measures, and thereby fuzzy sets, stand at the crossroads of these new approaches. Traditional views, interpretive settings and canonical experiments for the measurement of probability such as frequentist approaches, betting theories, comparative uncertainty relations are currently extended to the generalized uncertainty measures. These works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory; conversely Zadeh’s logical point of view on fuzzy sets suggests a set-theoretic perspective on uncertainty measures, that brings together numerical quantification and logic.