Abstract
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 is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)
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)
Jaynes, E.T., Bretthorst, G.L.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)
Mayer, G.: Interval Analysis and Automatic Result Verification. De Gruyter, Berlin (2017)
Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)
Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)
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)
Nguyen, H.T., Walker, C., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2019)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston, Dordrecht (1999)
Rabinovich, S.G.: Measurement Errors and Uncertainties: Theory and Practice. Springer, New York (2005)
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton (2011)
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)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Servin, C., Kosheleva, O., Kreinovich, V. (2021). Accuracy of Data Fusion: Interval (and Fuzzy) Case. In: Kreinovich, V., Hoang Phuong, N. (eds) Soft Computing for Biomedical Applications and Related Topics. Studies in Computational Intelligence, vol 899. Springer, Cham. https://doi.org/10.1007/978-3-030-49536-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-49536-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-49535-0
Online ISBN: 978-3-030-49536-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)