Advertisement

Probability, Possibility and Fuzzy Events

  • Eduardo Massad
  • Neli Regina Siqueira Ortega
  • Laecio Carvalho de Barros
  • Claudio José Struchiner
Chapter
  • 969 Downloads
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 232)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Eduardo Massad
    • 1
  • Neli Regina Siqueira Ortega
    • 1
  • Laecio Carvalho de Barros
    • 2
  • Claudio José Struchiner
    • 3
  1. 1.The University of São Paulo, São PauloBrazil
  2. 2.State University of Campinas, CampinasBrazil
  3. 3.PROCC, Rio de JaneiroBrazil

Personalised recommendations