A general information for fuzzy sets

  • P. Benvenuti
  • D. Vivona
  • M. Divari
6. Information
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)


In this paper we introduce a general definition of an information measure for fuzzy sets and we study its main properties. Then we describe a procedure to extend any information measure from a σ-algebra of ordinary sets to the σ-algebra of fuzzy sets of the same space.

Key Words

Information theory Fuzzy sets 


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  1. [1]
    P. Benvenuti — D. Vivona — M. Divari: Sull'integrale nella teoria dell'informazione, Rend. Mat. VII, 8, (1988) 31–43.Google Scholar
  2. [2]
    P. Benvenuti — D. Vivona — M. Divari: An integral for fuzzy sets in information theory, Proceedings of the 8th International Congress of Cybernetics and Systems, New York, June 1990 (to appear).Google Scholar
  3. [3]
    J. Kampé De Fériet — B. Forte: Information et probabilité, C.R.A.S., Paris, 265, (1967) 110–114, 142–146, 350–353.Google Scholar
  4. [4]
    J. Kampé De Fériet — P. Benvenuti: Sur une classe d'information, C.R.A.S., Paris, 269, (1969) 529–534.Google Scholar
  5. [5]
    G. J. Klir: Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?, F.S.S. 24, (1987) 141–160.Google Scholar
  6. [6]
    T. Murofushi: Two approaches to fuzzy measure theory: integrals based on pseudo-addition and Choquet's integral, Doctoral Thesis, Tokio Institute of Technology (1987).Google Scholar
  7. [7]
    H.T. Nguyen: On fuzziness and linguistic probabilities, JMAA 61, (1977) 658–671.Google Scholar
  8. [8]
    M. Sugeno: Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokio Institute of Technology (1974).Google Scholar
  9. [9]
    D. Vivona: L'informazione integrale, Quad. 19, I.M.A., Univ. Roma, (1982).Google Scholar
  10. [10]
    S. Weber: Decomposable measures and measures of information for crisp and fuzzy sets, Proc. of the I.F.A.C. Symposium, Marseille, july 1983.Google Scholar
  11. [11]
    L.A. Zadeh: Fuzzy sets, Inf. and Control 8, (1965) 338–353.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • P. Benvenuti
    • 1
  • D. Vivona
    • 1
  • M. Divari
    • 1
  1. 1.Dipartimento di Metodi e Modelli Matematici per le Scienze ApplicateUniversità di Roma “La Sapienza”Roma

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