Abstract
This paper deals with the aggregation of fuzzy relations under a closure constraint, that is, it studies how to combine a collection of fuzzy relations that present some common properties in order to obtain a single one with the same properties. This aggregation problem is addressed for two important classes of closely related fuzzy relations: generalized distances and indistinguishability operators.
Corresponding author
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Aczél. Lectures on Functional Equations and their Applications. Academic Press. New York. (1966).
C. Alsina and E. Trillas. “Synthesizing Implications”. International Journal of Intelligent Systems 7 (1992) 705–713.
B. De Baets and R. Mesiar, “Pseudo-metrics and T-equivalences”. J. Fuzzy Math, Vol. 5, No. 2 (1997) 471–481.
D. Dubois and H. Prade. “Aggregation of possibility measures”, in Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, J. Kacprzyk, M. Fedrizzi (eds), Kluwer Academic Publishers. (1990).
E. Klement, R. Mesiar and E. Pap. Triangular Norms. Kluwer Academic Publisher. (2000).
C.H. Ling. “Representation of Associative Functions”. Publ. Math. Debrecen 12 (1965) 189–212.
B. Schweizer and A. Sklar. Probabilistic Metric Spaces. North-Holland (1983).
E. Trillas and C. Alsina. Introducción a los espacios métricos generalizados. Serie Universitaria 49, Fund. Juan March. (in Spanish ). (1979).
E. Trillas. “Assaig sobre les relacions d’indistingibilitat”. Actes Congrés Català de Lògica, (1981) 51–59 (in Catalan).
E. Trillas and L. Valverde. “An Inquiry into Indistinguishability Operators”, in Aspects of Vagueness (Eds. H. Skala, S. Termini and E. Trillas), Kluwer, (1984) 231–256.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pradera, A., Trillas, E., Castiñeira, E. (2002). On the Aggregation of Some Classes of Fuzzy Relations. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 2. Studies in Fuzziness and Soft Computing, vol 90. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1796-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1796-6_10
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2504-6
Online ISBN: 978-3-7908-1796-6
eBook Packages: Springer Book Archive