Abstract
Recently, a new empirically successful algorithm was proposed for crisp clustering: the K-sets algorithm. In this paper, we show that a natural uncertainty-based formalization of what is clustering automatically leads to the mathematical ideas and definitions behind this algorithm. Thus, we provide an explanation for this algorithm’s empirical success.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
B.G. Buchanan, E.H. Shortliffe, Rule Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project (Addison-Wesley, Reading, 1984)
C.-S. Chang, W. Liao, Y.-S. Chen, L.-H. Liou, A mathematical theory for clustering in metric spaces. IEEE Trans. Netw. Sci. Eng. 3(1), 2–16 (2016)
E.T. Jaynes, G.L. Bretthorst, Probability Theory: The Logic of Science (Cambridge University Press, Cambridge, 2003)
G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic (Prentice Hall, Upper Saddle River, 1995)
H.T. Nguyen, V. Kreinovich, P. Wojciechowski, Strict Archimedean t-norms and t-conorms as universal approximators. Int. J. Approximate Reasoning 18(3–4), 239–249 (1998)
H.T. Nguyen, E.A. Walker, A First Course in Fuzzy Logic (Chapman and Hall/CRC, Boca Raton, 2006)
D.J. Sheskin, Handbook of Parametric and Nonparametric Statistical Procedures (Chapman and Hall/CRC, Boca Raton, 2011)
L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgements
This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation.
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., Sriboonchitta, S. (2020). Probabilistic and More General Uncertainty-Based (e.g., Fuzzy) Approaches to Crisp Clustering Explain the Empirical Success of the K-Sets Algorithm. 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_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-38893-5_4
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)