Top

Published in:

2018 | OriginalPaper | Chapter

On the Conflict Measures Agreed with the Combining Rules

Author : Alexander Lepskiy

Published in: Belief Functions: Theory and Applications

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The conflict measures induced by the conjunctive and disjunctive combining rules are studied in this paper in the framework of evidence theory. The coherence of conflict measures with combining rules is introduced and studied. In addition, the structure of conjunctive and disjunctive conflict measures is studied in the paper. In particular, it is shown that the metric and entropy components can be distinguished in such measures. Moreover, these components are changed differently after combining of the bodies of evidence.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Measuring Market Performance with Stochastic Demand: Price of Anarchy and Price of Uncertainty

next chapter Linear Belief Functions for Data Analytics

Bronevich, A., Lepskiy, A., Penikas, H.: The application of conflict measure to estimating incoherence of analyst’s forecasts about the cost of shares of Russian companies. Procedia Comput. Sci. 55, 1113–1122 (2015)CrossRef

Daniel, M.: Conflicts within and between belief functions. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS (LNAI), vol. 6178, pp. 696–705. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14049-5_71CrossRef

Dempster, A.P.: Upper and lower probabilities induced by multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)MathSciNetCrossRef

Destercke, S., Burger, T.: Toward an axiomatic definition of conflict between belief functions. IEEE Trans. Cybern. 43(2), 585–596 (2013)CrossRef

Dubois, D., Prade, H.: A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. Int. J. Gen. Syst. 12(3), 193–226 (1986)MathSciNetCrossRef

Dubois, D., Prade, H.: On the combination of evidence in various mathematical frameworks. In: Flamm, J., Luisi, T. (eds.) Reliability Data Collection and Analysis, pp. 213–241. Kluwer Acad. Publ., Dordrecht (1992)CrossRef

Florea, M.C., Jousselme, A.-L., Bossé, É., Grenier, D.: Robust combination rules for evidence theory. Inf. Fusion 10(2), 183–197 (2009)CrossRef

Jousselme, A.-L., Grenier, D., Bossé, É.: A new distance between two bodies of evidence. Inf. Fusion 2, 91–101 (2001)CrossRef

Lefèvre, E., Elouedi, Z.: How to preserve the conflict as an alarm in the combination of belief functions? Decis. Support Syst. 56, 326–333 (2013)CrossRef

10.

Lepskiy, A.: On internal conflict as an external conflict of a decomposition of evidence. In: Vejnarová, J., Kratochvíl, V. (eds.) BELIEF 2016. LNCS (LNAI), vol. 9861, pp. 25–34. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45559-4_3CrossRef

11.

Lepskiy, A.: Decomposition of evidence and internal conflict. Procedia Comput. Sci. 122, 186–193 (2017)CrossRef

12.

Liu, W.: Analysing the degree of conflict among belief functions. Artif. Intell. 170, 909–924 (2006)CrossRef

13.

Martin, A.: About conflict in the theory of belief functions. In: Denoeux, T., Masson, M.H. (eds.) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol. 164, pp. 161–168. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29461-7_19

14.

Schubert, J.: The internal conflict of a belief function. In: Denoeux, T., Masson, M.H. (eds.) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol. 164, pp. 169–177. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29461-7_20CrossRef

15.

Shafer, G.: A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton (1976)MATH

Title: On the Conflict Measures Agreed with the Combining Rules
Author: Alexander Lepskiy
Publisher: Springer International Publishing
Book: Belief Functions: Theory and Applications
Print ISBN: 978-3-319-99382-9

Electronic ISBN: 978-3-319-99383-6

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-99383-6_22

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner