Geometry of generators of triangular norms and copulas-Reference-Cited by-同舟云学术

Geometry of generators of triangular norms and copulas

Published:2024-01-01 Issue:1 Volume:12 Page:
ISSN:2300-2298
Container-title:Dependence Modeling
language:en
Short-container-title:

Author:

Houšková Kamila¹,Navara Mirko¹

Affiliation:

1. Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague , CZ-166 27 Prague , Czech Republic

Abstract

Abstract We study the relations between the shapes of strict triangular norms and their generators. The generators are not unique; to avoid this ambiguity, we introduce the class of balanced generators. We find conditions for their existence and a procedure of their computation. We formulate their influence on local properties of the corresponding triangular norms, in particular at the extremes of their domain. Many strict triangular norms are also copulas; thus, our results can also be applied to bivariate extreme value distributions described by some families of copulas.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/demo-2024-0004/pdf

Reference12 articles.

1. Genest, C., & Rivest, L.-P. (1989). A characterization of Gumbel’s family of extreme value distributions. Statistics & Probability Letters 8, 207–211.

2. Hájek, C. (1998). Metamathematics of Fuzzy Logic. Kluwer, Dordrecht.

3. Houšková, K. (2023). The Interplay of Triangular Norms and Their Generators. BSc. Thesis, Czech Technical University in Prague, Czech Republic.

4. Houšková, K., & Navara, M. (2023). Relations between the shapes of triangular norms and their generators. In: Durante, F., Saminger-Platz, S., Trutschnig, W., Vetterlein, T. (eds.) Copulas. Theory and Applications. 40th Linz Seminar on Fuzzy Set Theory (pp. 42–46), Linz, Austria: Johannes Kepler University.

5. Klement, E. P., Mesiar, R., & Pap, E. (2000). Triangular Norms. vol. 8 of Trends in Logic. Dordrecht, Netherlands: Kluwer Academic Publishers.