Modelling fraud detection by attack trees and Choquet integral
AbstractModelling an attack tree is basically a matter of associating a logical "and" and a logical "or" but in most of real world applications related to fraud management the "and/or"logic is not adequate to effectively represent the relationship between a parent node and its children, most of all when information about attributes is associated to the nodes and the main problem to solve is how to promulgate attribute values up the tree through recursive aggregation operations occurring at the "and/or"nodes. OWA-based aggregations have been introduced to generalize "and" and "or" operators starting from the observation that in between the extremes "or all"(and) and "or any"(or), terms (quantifiers) like "several" "most" "few" "some" etc. can be introduced to represent the different weights associated to the nodes in the aggregation. The aggregation process taking place at an OWA node depends on the ordered position of the child nodes but it doesn't take care of the possible interactions between the nodes. In this paper, we propose to overcome this drawback introducing the Choquet integral whose distinguished feature is to be able to take into account the interaction between nodes. At first, the attack tree is valuated recursively through a bottom-up algorithm whose complexity is linear versus the number of nodes and exponential for every node. Then, the algorithm is extended assuming that the attribute values in the leaves are unimodal LR fuzzy numbers and the calculation of Choquet integral is carried out using the alpha-cuts.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Computer and Management Sciences, University of Trento, Italy in its series DISA Working Papers with number 2011/09.
Length: 22 pages
Date of creation: Aug 2011
Date of revision: 31 Aug 2011
Postal: DISA Università degli Studi di Trento via Inama, 5 I-38122 Trento TN Italy
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-15 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008.
"A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package,"
European Journal of Operational Research,
Elsevier, vol. 186(2), pages 766-785, April.
- Michel Grabisch & Ivan Kojadinovic & Patrick Meyer, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00187175, HAL.
- Ghirardato, Paolo & Le Breton, Michel, 2000.
Journal of Economic Theory,
Elsevier, vol. 90(2), pages 277-285, February.
- GHIRARDATO, Paolo & LE BRETON, Michel, 1999. "Choquet rationality," CORE Discussion Papers 1999012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- GHIRARDATO, Paolo & LE BRETON, Michel, . "Choquet rationality," CORE Discussion Papers RP -1447, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
- Marc Roubens & Michel Grabisch, 1999.
"An axiomatic approach to the concept of interaction among players in cooperative games,"
International Journal of Game Theory,
Springer, vol. 28(4), pages 547-565.
- Grabisch, M. & Roubens, M., 1998. "An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games," Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie 9818, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
- Cardin, Marta & Giove, Silvio, 2008. "Aggregation Functions With Non-Monotonic Measures," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 0(2), pages 3-15, November.
- Michel Grabisch & Christophe Labreuche, 2010.
"A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid,"
UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers)
- Michel Grabisch & Christophe Labreuche, 2008. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00267932, HAL.
- Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003.
"On the extension of pseudo-Boolean functions for the aggregation of interacting criteria,"
European Journal of Operational Research,
Elsevier, vol. 148(1), pages 28-47, July.
- Michel Grabisch & Christophe Labreuche & Jean-Claude Vansnick, 2003. "On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria," Post-Print hal-00272780, HAL.
- De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Roberto Gabriele).
If references are entirely missing, you can add them using this form.