On the Computation of Uncertainty Measure in Dempster-Shafer Theory

Harmanec, David; Resconi, Germano; Klir, George J.; Pan, Yin

doi:10.1080/03081079608945140

Cited by 48 publications

(41 citation statements)

References 12 publications

(11 reference statements)

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“…Here S * − S * is considered as a non-specificity measure; and S * as a conflict measure 3 To use the maximum entropy in applications it is important to consider its calculus. Useful algorithms for computing S * were developed for the DST by Harmanec et al [27], for reachable interval-valued probability distributions by Abellán and Moral [2], and for the theory based on Choquet order-2 capacities (2-monotone measures) by Abellán and Moral [4].…”

Section: A Brief Overview Of Uncertainty Measuresmentioning

confidence: 99%

Classification with decision trees from a nonparametric predictive inference perspective

Abellán¹,

Baker²,

Coolen³

et al. 2014

Computational Statistics & Data Analysis

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Section: A Brief Overview Of Uncertainty Measuresmentioning

confidence: 99%

Classification with decision trees from a nonparametric predictive inference perspective

Abellán¹,

Baker²,

Coolen³

et al. 2014

Computational Statistics & Data Analysis

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show abstract

“…This functional can be readily generalized to any given convex set of probability distributions, as shown by Abellán and Moral (2003a). Useful algorithms for computing S * were developed for the DST by Harmanec et al (1996), for reachable interval-valued probability distributions by Abellán and Moral (2003a), and for the theory based on Choquet order-2 capacities (2-monotone measures) by .…”

Section: An Overview Of Uncertainty Measuresmentioning

confidence: 99%

Uncertainty measures on probability intervals from the imprecise Dirichlet model

Abellán

2006

International Journal of General Systems

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When we use a mathematical model to represent information, we can obtain a closed and convex set of probability distributions, also called a credal set. This type of representation involves two types of uncertainty called conflict (or randomness) and non-specificity, respectively. The imprecise Dirichlet model (IDM) allows us to carry out inference about the probability distribution of a categorical variable obtaining a set of a special type of credal set (probability intervals). In this paper, we shall present tools for obtaining the uncertainty functions on probability intervals obtained with the IDM, which can enable these functions in any application of this model to be calculated.

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“…Fortunately, a relatively simple algorithm for computing S * in DST was developed and its correctness proven (Meyerowitz et al 1994 andHarmanec et al 1996). It was initially assumed, but not proven, that the use of the algorithm can be extended for computing the upper entropy of any credal set (Klir 2003).…”

Section: Upper Entropymentioning

confidence: 99%

Disaggregated total uncertainty measure for credal sets

Abellán

Klir

Moral

2006

International Journal of General Systems

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We present a new approach to measure uncertainty/information applicable to theories based on convex sets of probability distributions, also called credal sets. A definition of a total disaggregated uncertainty measure on credal sets is proposed in this paper motivated by recent outcomes. This definition is based on the upper and lower values of Shannon's entropy for a credal set. We justify the use of the proposed total uncertainty measure and the parts into which it is divided: the maximum difference of entropies, which can be used as a non-specificity measure (imprecision), and the minimum of entropy, which represents a measure of conflict (contradiction).

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On the Computation of Uncertainty Measure in Dempster-Shafer Theory

Cited by 48 publications

References 12 publications

Classification with decision trees from a nonparametric predictive inference perspective

Classification with decision trees from a nonparametric predictive inference perspective

Uncertainty measures on probability intervals from the imprecise Dirichlet model

Disaggregated total uncertainty measure for credal sets

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