Fuzzy Events, Fuzzy Probability and Applications in Economic and Social Sciences

Abstract

In the subjective approach to the theory of probability, conditional events are always considered as propositions in a three valued logic (De Finetti in Teoria delle probabilità. Einaudi Editore, Torino, 1970; Coletti and Scozzafava in Probabilistic logic in a coherent setting. Kluwer Academic Publishers, London, 2002). Assuming a particular algebraic representation, we propose a definition of fuzzy event that generalizes the concepts of conditional event. Moreover we present some applications of fuzzy events in Social Science, e.g. in Decision Making under uncertainty. Generalizing the subjective approach to conditional probability by De Finetti, we propose some possible subjective definitions of fuzzy probability that are coherent with the axiomatic approach by Dubins to the finitely additive conditional probability. We propose some interpretations of fuzzy probability in Social Sciences, e.g. as an extension of a utility function. Finally, we explore some possible extensions of such concepts, defining fuzzy event and fuzzy probability of type 2 and we look for possible applications in Social Sciences, in particular in fuzzy decision making.