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International Conference on Scalable Uncertainty Management

SUM 2018: Scalable Uncertainty Management pp 321–332Cite as

A New Measure of General Information on Pseudo Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11142))

Abstract

The setting of this paper is the general information theory and the pseudo-analysis. We consider the general information measure J, defined without probability for crisp sets or without fuzzy measure for fuzzy sets and we propose a particular information measure for intersection of two sets. The pseudo-analysis is used to generalize the definition of independence and it leads to a functional equation. This equation belongs to a system of functional equations. We present some solutions of this system.

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References

  1. Aczel, J.: Lectures on Functional Equations and Their Applications. Academic Press, New York (1966)

    MATH  Google Scholar 

  2. Benvenuti, P.: Sulle misure di informazione compositive con traccia compositiva unversale. Rendiconti di Matematica 2(3–4), 481–505 (1969). Serie IV

    Google Scholar 

  3. Benvenuti, P.: Sur l’independence dans l’information, Colloquies Internationaux du C.N.R.S. N.276 - Theorie De l’Information, pp. 49–55 (1974)

    Google Scholar 

  4. Benvenuti, P., Divari, M., Pandolfi, M.: Su un sistema di equazioni funzionali provenienti dalla teoria soggettiva dell’informazione. Rendiconti di Matematica 5(39), 529–540 (1972). Serie VI

    MATH  Google Scholar 

  5. Benvenuti, P., Mesiar, R., Vivona, D.: Handbook of Measure, chap. 33, Monotone set-functions-based integrals, pp. 1331–1379 (2002)

    Google Scholar 

  6. Forte, B.: Measures of information: the general axiomatic theory, R.A.I.R.O. Informatique Théorique et Appl. 63–90 (1969)

    Google Scholar 

  7. Halmos, P.R.: Measure Theory. Princeton, Van Nostrand Company (1966)

    Google Scholar 

  8. De Feriét, J.K., Forte, B.: Information et Probabilité. Comptes Rendue de L’Académie des Sci. Paris 265, 110–114, 142–146, 350–353 (1967)

    Google Scholar 

  9. Mesiar, R., Rybarik, J.: Pseudo-aritmetical operations, Tatra. Mount. Math. Publ. 2, 185–192 (1993)

    MATH  Google Scholar 

  10. Pap, E.: g-calculus Zr. Rad 23(1), 145–156 (1993)

    MathSciNet  MATH  Google Scholar 

  11. Pap, E.: Null-Additive Set Function. Kluver Academic Publishers, Dordrect (1995)

    MATH  Google Scholar 

  12. Vivona, D., Divari, M.: An independence property for genenral information. Nat. Sci. 8, 66–69 (2016). https://doi.org/10.4236/ns.2016.82008

    Article  Google Scholar 

  13. Vivona, D., Divari, M.: Pseudo-analysis: some measures of general information. In: IEEE 14th International Symposium on Intelligent Systems and Informatics, SISY 2016, 29–31 August 2016, Subotica, Serbia, pp. 141–144 (2016)

    Google Scholar 

  14. Vivona, D., Divari, M.: Pseudo-analysis: some measures of general conditional information. Adv. Sci. Technol. Eng. Syst. J. 2(n2), 36–40 (2016)

    Article  Google Scholar 

  15. Vivona, D., Divari, M.: On the functional equation: \(F(x, y) \oplus z = F(x \oplus z, y \oplus z)\). Int. J. Pure Math. (2018, submitted)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Civil and Industrial Engineering, Department of Basic and Applied Sciences for Engineering, “Sapienza” University of Rome, Roma, Italy

    Doretta Vivona

  2. via Borgorose, Roma, Italy

    Maria Divari

Authors
  1. Doretta Vivona
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  2. Maria Divari
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Corresponding author

Correspondence to Doretta Vivona .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  3. Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

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Vivona, D., Divari, M. (2018). A New Measure of General Information on Pseudo Analysis. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_22

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  • DOI: https://doi.org/10.1007/978-3-030-00461-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00460-6

  • Online ISBN: 978-3-030-00461-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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