Measuring Total Uncertainty in Dempster-Shafer Theory: A Novel Approach

Moral

2003

Int. J. Intell. Syst.

122

We present an application of the measure of total uncertainty on convex sets of probability distributions, also called credal sets, to the construction of classification trees. In these classification trees the probabilities of the classes in each one of its leaves is estimated by using the imprecise Dirichlet model. In this way, smaller samples give rise to wider probability intervals. Branching a classification tree can decrease the entropy associated with the classes but, at the same time, as the sample is divided among the branches the nonspecificity increases. We use a total uncertainty measure (entropy ϩ nonspecificity) as branching criterion. The stopping rule is not to increase the total uncertainty. The good behavior of this procedure for the standard classification problems is shown. It is important to remark that it does not experience of overfitting, with similar results in the training and test samples.

Section: Total Uncertainty On Credal Setsmentioning

confidence: 94%

Building classification trees using the total uncertainty criterion

Moral

2003

Int. J. Intell. Syst.

122

“…In the early 1990s, the unsuccessful attempts to find a generalized Shannon entropy in the DST were replaced with attempts to find an aggregated measure of both types of uncertainty (Harmanec and Klir 1994). An aggregate measure that satisfies all the required properties (additivity, subadditivity, monotonicity, proper range, etc.)…”

Section: An Overview Of Uncertainty Measuresmentioning

confidence: 99%

Uncertainty measures on probability intervals from the imprecise Dirichlet model

International Journal of General Systems

2006

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.

“…A summary of these unsuccessful efforts is given in Klir and Wierman (1998) and Klir (2006). The unsuccessful attempts to find a justifiable generalization of the Shannon entropy in DST were eventually replaced with attempts to find an aggregated measure of both nonspecificity and conflict (Harmanec and Klir 1994). Such a measure, which satisfies all the required properties, was found around the mid 1990s by several authors (see Klir (2006) for more details).…”

Section: Uncertainty In Dempster -Shafer Theorymentioning

confidence: 99%

“…In the particular case of belief functions, Harmanec and Klir (1994) have already considered that upper entropy is a measure of aggregated total uncertainty. They justify it by using an axiomatic approach.…”

Section: Upper Entropymentioning

confidence: 99%

Disaggregated total uncertainty measure for credal sets

International Journal of General Systems

Klir

Moral

2006

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).