Probability, possibility and fuzzy events

Abstract

It is very common to confuse fuzzy sets theory with the theory of probabilities. Frequently membership degree is misinterpreted as probability value and the membership function as a statistic distribution function. This confusion emerges due to the fact that there is a narrow relationship among the two theories and, under certain aspects, the fuzzy theory presents characteristics very similar to the probability theory. In fact, its possible to see from the theory of measures that the probability measure is a particular case of fuzzy measure (Klir & Yuan, 1995; Pedrycz & Gomide, 1998 and 2007; Barros & Bassanezi, 2006). Nevertheless, it is important to understand the differences between these theories for best comprehend how they can be complementary, and how they can work together, as interesting and powerful mathematical tools. © 2008 Springer-Verlag Berlin Heidelberg.