Abstract
In principle, in applications of fuzzy techniques, we can have different complex membership functions. In many practical applications, however, it turns out that to get a good quality result – e.g., a good quality control – it is sufficient to consider simple triangular and trapezoid membership functions. There exist explanations for this empirical phenomenon, but the existing explanations are rather mathematically sophisticated and are, thus, not very intuitively clear. In this paper, we provide a simple – and thus, more intuitive – explanation for the ubiquity of triangular and trapezoid membership functions.
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
Similar content being viewed by others
References
R. Belohlavek, J.W. Dauben, G.J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective (Oxford University Press, New York, 2017)
G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic (Prentice Hall, Upper Saddle River, New Jersey, 1995)
O. Kosheleva, V. Kreinovich, Why triangular membership functions are often efficient in F-transform applications: relation to probabilistic and interval uncertainty and to Haar wavelets, in Proceedings of the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU’2018, ed. by J. Medina, et al., Spain, 11–15 June 2018
O. Kosheleva, V. Kreinovich, S. Shahbazova, Type-2 fuzzy analysis explains ubiquity of triangular and trapezoid membership functions, in Proceedings of the 7th World Conference on Soft Computing, Baku, Azerbaijan, 29–31 May 2018
J.M. Mendel, Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions (Springer, Cham, Switzerland, 2017)
J.M. Mendel, D. Wu, Perceptual Computing: Aiding People in Making Subjective Judgments (IEEE Press and Wiley, New York, 2010)
H.T. Nguyen, E.A. Walker, A First Course in Fuzzy Logic (Chapman and Hall/CRC, Boca Raton, FL, 2006)
V. Novák, I. Perfilieva, J. Močkoř, Mathematical Principles of Fuzzy Logic (Kluwer, Boston, Dordrecht, 1999)
L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgements
This work was supported in part by the National Science Foundation grant HRD-1242122 (Cyber-ShARE Center of Excellence). The authors are thankful to all the participants of the 7th World Conference on Soft Computing (Baku, Azerbaijan, May 29–31, 2018) for valuable discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kreinovich, V., Kosheleva, O., Shahbazova, S.N. (2020). Why Triangular and Trapezoid Membership Functions: A Simple Explanation. In: Shahbazova, S., Sugeno, M., Kacprzyk, J. (eds) Recent Developments in Fuzzy Logic and Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 391. Springer, Cham. https://doi.org/10.1007/978-3-030-38893-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-38893-5_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38892-8
Online ISBN: 978-3-030-38893-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)