Abstract
In the non-fuzzy (e.g., interval) case, if two expert’s opinions are consistent, then, as the result of fusing the knowledge of these two experts, we take the intersection of the two sets (e.g., intervals) describing the expert’s opinions. In the experts are inconsistent, i.e., if the intersection is empty, then a reasonable idea is to assume that at least one of these experts is right, and thus, to take the union of the two corresponding sets. In practice, expert opinions are often imprecise; this imprecision can be naturally described in terms of fuzzy logic – a technique specifically designed to describe such imprecision. In the fuzzy case, expert opinions are not always absolutely consistent or absolutely inconsistent, they may be consistent to a certain degree. In this case, we show how the above natural idea of fusing expert opinions can be extended to the fuzzy case. As a result, we, in general, get not “and” (which would correspond to the intersection), not “or” (which would correspond to the union), but rather an appropriate fuzzy combination of “and”- and “or”-operations.
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)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)
Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)
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 (1999)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgments
This work was supported in part by the US National Science Foundation via grant HRD-1242122 (Cyber-ShARE Center of Excellence).
The authors are thankful to the anonymous referees for valuable suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Servin, C., Kosheleva, O., Kreinovich, V. (2019). How to Fuse Expert Knowledge: Not Always “And” but a Fuzzy Combination of “And” and “Or”. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-21920-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21919-2
Online ISBN: 978-3-030-21920-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)