Abstract
The strongest and the weakest t-norms that coincide with the given t-norm on a subregion of the unit interval are discussed. The question whether such a t-norm can be obtained as a limit of the sequence of continuous t-norms that coincide with the original t-norm on the given subregion is investigated.
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
References
Alsina, C., Frank, M.J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas. World Scientific, Singapore (2006)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer-Verlag, New York (2007)
Clifford, A.H.: Naturally totally ordered commutative semigroups. Am. J. Math. 76, 631–646 (1954)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)
Hájek, P.: Metamathematics of fuzzy logic. Kluwer Academic Publishers, Dordrecht (1998)
Jenei, S.: A note on the ordinal sum theorem and its consequence for the construction of triangular norms. Fuzzy Sets Syst. 126, 199–205 (2002)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)
Mesiar, R., Baets, B. D.: New construction methods for aggregation operators. In: IPMU 2000, pp. 701–706. Madrid (2000)
Mesiarová-Zemánková A.: Continuous completions of triangular norms known on a subregion of the unit interval, Fuzzy Sets and Systems. http://www.mat.savba.sk/zemankova/unpublished.htm
Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York (1983)
Sugeno, M.: Industrial Applications of Fuzzy Control. Elsevier, New York (1985)
Acknowledgement
This work was supported by grant VEGA 2/0049/14 and Program Fellowship of SAS.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Mesiarová-Zemánková, A. (2015). Extremal Completions of Triangular Norms Known on a Subregion of the Unit Interval. In: Torra, V., Narukawa, T. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2015. Lecture Notes in Computer Science(), vol 9321. Springer, Cham. https://doi.org/10.1007/978-3-319-23240-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-23240-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23239-3
Online ISBN: 978-3-319-23240-9
eBook Packages: Computer ScienceComputer Science (R0)