Search

Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from an abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of uncertainty of the extensions considering that the probability values of the arguments are imprecise. We use credal sets to model the uncertainty values of arguments and from these credal sets, we calculate the lower and upper bounds of the extensions. We study some properties of the suggested approach and illustrate it with an scenario of decision making. more...

Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is based on the polarity theory for closed convex cones. Learning from this simple observation, in this paper we introduce a new (lexicographic) polarity theory for general convex cones and then we apply it in order to establish an analogous correspondence between coherent sets of desirable gambles and convex sets of lexicographic probabilities. more...

Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is based on the polarity theory for closed convex cones. Learning from this simple observation, in this paper we introduce a new (lexicographic) polarity theory for general convex cones and then we apply it in order to establish an analogous correspondence between coherent sets of desirable gambles and convex sets of lexicographic probabilities. more...

We elaborate on hierarchical credal sets, which are sets of probability mass functions paired with second-order distributions. A new criterion to make decisions based on these models is proposed. This is achieved by sampling from the set of mass functions and considering the Kullback-Leibler divergence from the weighted center of mass of the set. We evaluate this criterion in a simple classification scenario: the results show performance improvements when compared to a credal classifier where the second-order distribution is not taken into account. more...

We propose the use of evidential combination operators for advanced driver assistance systems (ADAS) for vehicles. More specifically, we elaborate on how three different operators, one precise and two imprecise, can be used for the purpose of entrapment prediction, i.e., to estimate when the relative positions and speeds of the surrounding vehicles can potentially become dangerous. We motivate the use of the imprecise operators by their ability to model uncertainty in the underlying sensor information and we provide an example that demonstrates the differences between the operators., Springer ChamThis work was supported by the Information Fusion Research Program (University of Skövde, Sweden), in partnership with the Swedish Knowledge Foundation under grant 2010-0320 (URL: http://www.infofusion.se, UMIF project). more...

We elaborate on hierarchical credal sets, which are sets of probability mass functions paired with second-order distributions. A new criterion to make decisions based on these models is proposed. This is achieved by sampling from the set of mass functions and considering the Kullback-Leibler divergence from the weighted center of mass of the set. We evaluate this criterion in a simple classification scenario: the results show performance improvements when compared to a credal classifier where the second-order distribution is not taken into account. more...

We utilize second-order probability distributions for modeling second-order information over imprecise evidence in the form of credal sets. We generalize the Dirichlet distribution to a shifted version, denoted the S-Dirichlet, which allows one to restrict the support of the distribution by lower bounds. Based on the S-Dirichlet distribution, we present a simple combination schema denoted as second-order credal combination (SOCC), which takes second-order probability into account. The combination schema is based on a set of particles, sampled from the operands, and a set of weights that are obtained through the S-Dirichlet distribution. We show by examples that the second-order probability distribution over the imprecise joint evidence can be remarkably concentrated and hence that the credal combination operator can significantly overestimate the imprecision. more...

We present an experiment for evaluating precise and imprecise evidential combination operators. The experiment design is based on the assumption that only limited statistical information is available in the form of multinomial observations. We evaluate three different evidential combination operators; one precise, the Bayesian combination operator, and two imprecise, the credal and Dempster’s combination operator, for combining independent pieces of evidence regarding some discrete state space of interest. The evaluation is performed by using a score function that takes imprecision into account. The results show that the precise framework seems to perform equally well as the imprecise frameworks. more...

We utilize second-order probability distributions for modeling second-order information over imprecise evidence in the form of credal sets. We generalize the Dirichlet distribution to a shifted version, denoted the S-Dirichlet, which allows one to restrict the support of the distribution by lower bounds. Based on the S-Dirichlet distribution, we present a simple combination schema denoted as second-order credal combination (SOCC), which takes second-order probability into account. The combination schema is based on a set of particles, sampled from the operands, and a set of weights that are obtained through the S-Dirichlet distribution. We show by examples that the second-order probability distribution over the imprecise joint evidence can be remarkably concentrated and hence that the credal combination operator can significantly overestimate the imprecision. more...

We are interested in whether or not there exist any advantages of utilizing credal set theory for the discrete state estimation problem. We present an experiment where we compare in total six different methods, three based on Bayesian theory and three on credal set theory. The results show that Bayesian updating performed on centroids of operand credal sets significantly outperforms the other methods. We analyze the result based on degree of imprecision, position of extreme points, and second-order distributions. more...

We present a variation of a method of classification based in uncertainty on credal set. Similarly to its origin it use the imprecise Dirichlet model to create the credal set and the same uncertainty measures. It take into account sets of two variables to reduce the uncertainty and to seek the direct relations between the variables in the data base and the variable to be classified. The success are equivalent to the success of the first method except in those where there are a direct relations between some variables that decide the value of the variable to be classified where we have a notable improvement. more...