Abstract
The article introduces and discusses threshold belief and plausibility functions. When forming such functions, only focal elements that are “significant” for a given set are taken into account. The significance of focal elements is determined using a similarity measure and a threshold. Threshold functionals of uncertainty, external and internal conflicts, threshold rules of combination are introduced and considered on the basis of threshold functions of the theory of evidence. A number of examples are given to illustrate the use of threshold tools.
The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE University) in 2024.
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References
Bronevich, A., Lepskiy, A.: Imprecision indices: axiomatic, properties and applications. Int. J. Gen. Syst. 44(7–8), 812–832 (2015)
Coletti, G., Bouchon-Meunier, B.: A study of similarity measures through the paradigm of measurement theory: the classic case. Soft Comput. 23, 6827–6845 (2019)
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_71
Deng, Y.: Generalized evidence theory. Appl. Intell. 43, 530–543 (2015)
Denneberg, D., Grabisch, M.: Interaction transform of set functions over a finite set. Inf. Sci. 121, 149–170 (1999)
Dubois, D., Prade, H.: A set-theoretic view on belief functions: logical operations and approximations by fuzzy sets. Int. J. Gen. Syst. 12, 193–226 (1986)
Lepskiy, A.: Analysis of information inconsistency in belief function theory. Part I: external conflict. Control Sci. 5, 2–16 (2021)
Lepskiy, A.: Analysis of information inconsistency in belief function theory. Part II: internal conflict. Control Sci. 6, 2–12 (2021)
Lepskiy, A.: Conflict measure of belief functions with blurred focal elements on the real line. In: Denœux, T., Lefèvre, E., Liu, Z., Pichon, F. (eds.) BELIEF 2021. LNCS (LNAI), vol. 12915, pp. 197–206. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88601-1_20
Shafer, G.: A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton (1976)
Smets, P.: Decision making in TBM: the necessity of the pignistic transformation. Int. J. Approx. Res. 38, 133–147 (2005)
Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–243 (1994)
Zhang, L.: Representation, independence and combination of evidence in the Dempster-Shafer theory. In: Yager, R.R., et al. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 51–69. John Wiley & Sons, New York (1994)
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Lepskiy, A. (2024). Threshold Functions and Operations in the Theory of Evidence. In: Bi, Y., Jousselme, AL., Denoeux, T. (eds) Belief Functions: Theory and Applications. BELIEF 2024. Lecture Notes in Computer Science(), vol 14909. Springer, Cham. https://doi.org/10.1007/978-3-031-67977-3_23
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DOI: https://doi.org/10.1007/978-3-031-67977-3_23
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