Abstract
The aim of the work is to involve fuzzy equivalence relations and aggregation of corresponding equivalence relations in a clustering process. Namely, we introduce fuzzy equivalence relations for different attributes of objects and then we aggregate these fuzzy equivalence relations to determine the similarities of objects. It is possible to involve different weights for attributes, thus defining the importance attributes in decision making process. In the work we also present illustrative examples.
The work has been supported by European Regional Development Fund within the project Nr.1.1.1.2/16/I/001, application Nr.1.1.1.2/VIAA/4/20/707 “Fuzzy relations and fuzzy metrics for customer behavior modeling and analyis”.
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
De Baets, B., Mesiar, R.: Pseudo-metrics and \(T\)-equivalences. J. Fuzzy Math. 5, 471–481 (1997)
Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy C-means clustering algorithm. Comput. Geosci. 10, 191–203 (1984)
Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Springer, Cham (2005). https://doi.org/10.1007/b106267
Bodenhofer, U.: A similarity-based generalization of fuzzy orderings preserving the classical axioms. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 8(5), 593–610 (2000)
Klement, E.P., Mesiar, R., Pap, E.: Generated triangular norms. Kibernetika 36, 363–377 (2000)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishing, Dodrecht (2000)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper II. General constructions and parametrized families. Fuzzy Sets Syst. 145, 411–438 (2004)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms: basic notions and properties. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms, pp. 17–60. Elsevier, Amsterdam (2005)
Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions (Encyclopedia of Mathematics and its Applications). Cambridge University Press, Cambridge (2009)
Mesiar, R., Calvo, T., Mayor, G.: Aggregation Operators: New Trends and Applications (Studies in Fuzziness and Soft Computing). Physica-Verlag, Heidelberg (2002)
Saminger, S., Mesiar, R., Bodenhofer, U.: Domination of aggregation operators and preservation of transitivity. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 10(Suppl.), 11–35 (2002)
Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3, 177–200 (1971)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Grigorenko, O., Mihailovs, V. (2022). Aggregated Fuzzy Equivalence Relations in Clustering Process. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_37
Download citation
DOI: https://doi.org/10.1007/978-3-031-08971-8_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-08970-1
Online ISBN: 978-3-031-08971-8
eBook Packages: Computer ScienceComputer Science (R0)