Accuracy of Data Fusion: Interval (and Fuzzy) Case

  • Christian Servin
  • Olga Kosheleva
  • Vladik KreinovichEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 899)


The more information we have about a quantity, the more accurately we can estimate this quantity. In particular, if we have several estimates of the same quantity, we can fuse them into a single more accurate estimate. What is the accuracy of this estimate? The corresponding formulas are known for the case of probabilistic uncertainty. In this paper, we provide similar formulas for the cases of interval and fuzzy uncertainty.



This work was supported in part by the National Science Foundation via grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence).


  1. 1.
    Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)CrossRefGoogle Scholar
  2. 2.
    Jaulin, L., Kiefer, M., Didrit, O., Walter, E.: Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control, and Robotics. Springer, London (2001)zbMATHGoogle Scholar
  3. 3.
    Jaynes, E.T., Bretthorst, G.L.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)CrossRefGoogle Scholar
  4. 4.
    Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)zbMATHGoogle Scholar
  5. 5.
    Mayer, G.: Interval Analysis and Automatic Result Verification. De Gruyter, Berlin (2017)CrossRefGoogle Scholar
  6. 6.
    Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)CrossRefGoogle Scholar
  7. 7.
    Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)CrossRefGoogle Scholar
  8. 8.
    Nguyen, H.T., Kreinovich, V.: Nested intervals and sets: concepts, relations to fuzzy sets, and applications. In: Kearfott, R.B., Kreinovich, V. (eds.) Applications of Interval Computations, pp. 245–290. Kluwer, Dordrecht (1996)CrossRefGoogle Scholar
  9. 9.
    Nguyen, H.T., Walker, C., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2019)zbMATHGoogle Scholar
  10. 10.
    Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston, Dordrecht (1999)CrossRefGoogle Scholar
  11. 11.
    Rabinovich, S.G.: Measurement Errors and Uncertainties: Theory and Practice. Springer, New York (2005)zbMATHGoogle Scholar
  12. 12.
    Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton (2011)zbMATHGoogle Scholar
  13. 13.
    Walster, G.W., Kreinovich, V.: For unknown-but-bounded errors, interval estimates are often better than averaging. ACM SIGNUM Newsl. 31(2), 6–19 (1996)CrossRefGoogle Scholar
  14. 14.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  • Christian Servin
    • 1
  • Olga Kosheleva
    • 2
  • Vladik Kreinovich
    • 2
    Email author
  1. 1.Computer Science and Information Technology Systems DepartmentEl Paso Community CollegeEl PasoUSA
  2. 2.University of Texas at El PasoEl PasoUSA

Personalised recommendations