Advertisement

Abstract

The aim of this paper is to give, on the fuzzy setting, a definition of fuzziness for the information without probability or fuzzy measure (general information).

Moreover, we present a class of measures of fuzziness, solving a system of functional conditions coming from the properties of fuzziness.

Keywords

Information Theory Functional Condition Fuzzy Logic Functional Equation Mathematical Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aczél J.: Functional equations and their applications. Academic Press (1966)Google Scholar
  2. 2.
    Ebanks, B.R.: On measures of fuzziness and Their representations. J. Math. An. Appl. 94, 24–37 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Benvenuti, P., Vivona, D., Divari, M.: A General Information for Fuzzy Sets. In: Bouchon-Meunier, B., Zadeh, L.A., Yager, R.R. (eds.) IPMU 1990. LNCS, vol. 521, pp. 307–316. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  4. 4.
    Couso, I., Gil, P., Montes, S.: Measures of fuzziness and Information Theory. In: Proc. IPMU 1996, pp. 501–505 (1996)Google Scholar
  5. 5.
    DeLuca, A., Termini, S.: A definition of non probabilistic entropy in the setting of fuzzy sets theory. Inform. and Control 20, 301–312 (1972)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Klir, G.J., Folger, T.A.: Fuzzy sets, Uncertainty, and Information. Prentice-Hall International editions (1988)Google Scholar
  7. 7.
    Kosko, B.: Fuzzy Thinking: The New Science of Fuzzy Logic, Hyperion Eds. (1993)Google Scholar
  8. 8.
    Zadeh, L.A.: Fuzzy sets. Inf. and Control 8, 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Doretta Vivona
    • 1
  • Maria Divari
    • 2
  1. 1.Dip. SBAISapienza Universitá di RomaRomaItaly
  2. 2.Sapienza Universitá di RomaRomaItaly

Personalised recommendations