The Normalization of the Dempster’s Rule of Combination

Sevastjanov, Pavel; Bartosiewicz, Paweł; Tkacz, Kamil

doi:10.1007/978-3-642-13232-2_81

Cited by 2 publications

(1 citation statement)

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“…Within the framework of the transferable belief model (TBM), Denoeux extended the main concepts of DST, which include credibility, plausibility, combination and normalization which lay the theoretical foundations of IBS. Most research fields of IBS involve combination rule (Fu & Yang 2012, 2011Sevastianov 2012;Song et al 2014;Wang 2007), normalization (Sevastjanov et al 2010;Xu et al 2012), and uncertainty measure (Jiang 2017;Son 2016). However, few are concerned with the distance within the framework of IBS.…”

Section: Introductionmentioning

confidence: 99%

A Distance Measure of Interval-valued Belief Structures

Cao¹,

Zhang²,

Feng³

2019

JSM

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Interval-valued belief structures are generalized from belief function theory, in terms of basic belief assignments from crisp to interval numbers. The distance measure has long been an essential tool in belief function theory, such as conflict evidence combinations, clustering analysis, belief function and approximation. Researchers have paid much attention and proposed many kinds of distance measures. However, few works have addressed distance measures of interval-valued belief structures up. In this paper, we propose a method to measure the distance of interval belief functions. The method is based on an interval-valued one-dimensional Hausdorff distance and Jaccard similarity coefficient. We show and prove its properties of non-negativity, non-degeneracy, symmetry and triangle inequality. Numerical examples illustrate the validity of the proposed distance.

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