Monte-Carlo Estimations for Belief Functions

Kramosil, Ivan

doi:10.1007/978-1-4615-0587-7_13

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“…To overcome these computational limitations, different approximation methods have been proposed. Some are based on Monte-Carlo techniques [3], [4], [5], while others seek to restrict the number of focal elements [6], [7], often by mapping belief functions to probability measures (Bayesian approximation or probability transformation [8], [9], [10], [11]), as the latter have a number of focal elements which is linear in the size of the frame of discernment.…”

Section: Introductionmentioning

confidence: 99%

$L_{p}$ Consonant Approximations of Belief Functions

Cuzzolin

2014

IEEE Trans. Fuzzy Syst.

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In this paper we solve the problem of approximating a belief measure with a necessity measure or "consonant belief function" in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: partial approximations are first sought in each component of the complex, while global solutions are selected among them. As a first step in this line of study, we seek here approximations which minimize L p norms. Approximations in the mass space can be interpreted in terms of mass redistribution, while approximations in the belief space generalize the maximal outer consonant approximation. We compare them with each other and with other classical approximations, and illustrate them with the help of a running example. Index TermsTheory of evidence, possibility theory, consonant belief functions, geometric approach, simplicial complex, (outer) consonant approximation, isopignistic function, L p norms.

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Section: Introductionmentioning

confidence: 99%

$L_{p}$ Consonant Approximations of Belief Functions

Cuzzolin

2014

IEEE Trans. Fuzzy Syst.

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show abstract

Monte-Carlo Estimations for Belief Functions

Cited by 1 publication

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$L_{p}$ Consonant Approximations of Belief Functions

$L_{p}$ Consonant Approximations of Belief Functions

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