In this paper we prove that a recent Bayesian approximation of belief functions, the relative belief of singletons, meets a number of properties with respect to Dempster’s rule of combination which mirrors those satisfied by the relative plausibility of singletons. In particular, its operator commutes with Dempster’s sum of plausibility functions, while perfectly representing a plausibility fun...

Abstrac t . In probabilistic reasoning when we have to build a probability distribution on some events and no further information is available, we then apply the insufficient reasoning principle; i.e. we assume that the events have equal opportunities to occur. In our previous work we have observed that in the Dempster-Shafer theory of evidence the principle is not applied when using Dempster's...

Evolutionary optimization (EO) has been proven to be highly effective computation means in solving asymmetry problems engineering practices. In this study, a novel evolutionary approach for the belief rule base (BRB) system is proposed, namely EO-BRB, by constructing an model and employing Differential (DE) algorithm as its engine due ability locate optimal solution with nonlinear complexity. E...

While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the contexts of use of these theory are notably different and the semantics behind these theories are not exactly the same. A prominent issue is increasingly rega...

We study a new approach to regression analysis. We propose a new rule-based regression model using the theoretical framework of belief functions. For this purpose we use the recently proposed Evidential c-means (ECM) to derive rule-based models solely from data. ECM allocates, for each object, a mass of belief to any subsets of possible clusters, which allows to gain a deeper insight on the dat...

Based on the canonical decomposition of belief functions, Smets introduced the concept of a latent belief structure (LBS). This concept is revisited in this article. The study of the combination of LBSs allows us to propose a less committed version of Dempster’s rule, resulting in a commutative, associative and idempotent rule of combination for LBSs. This latter property makes it suitable to c...

The theory of belief networks offers a relatively new approach for dealing with uncertain information in knowledge-based (expert) systems. In contrast with the heuristic techniques for reasoning with uncertainty employed in many rule-based expert systems, the theory of belief networks is mathematically sound, based on techniques from probability theory. It therefore seems attractive to convert ...

In previous work [8] we proposed an extension for the belief base of AgentSpeak agents based on Description Logic, aiming at enabling agent oriented programming to cope with recently proposed technologies for the Semantic Web. In such an extension an agent belief base contains the definition of complex concepts, besides specific factual knowledge. The foreseen advantages are: (i) more expressiv...