Jörg Gebhardt

The context model: An integrating view of vagueness and uncertainty

Abstract The problem of handling vagueness and uncertainty as two different kinds of partial ignorance has become a major issue in several fields of scientific research. Currently the most popular approaches are Bayes theory, Shafers evidence theory, the transferable belief model, and the possibility theory with its relationships to fuzzy sets. Since the justification of some of the mentioned theories has not been clarified for a long time, some criticism on these models is still pending. For that reason we have developed a model of vagueness and uncertainty—called the context model—that provides a formal environment for the comparison and semantic foundation of the referenced theories. In this paper we restrict ourselves to the presentation of basic ideas keyed to the interpretation of Bayes theory and the Dempster-Shafer theory within the context model. Furthermore the context model is applied to show a direct comparison of these two approaches based on the well-known spoiled sandwich effect, the three prisoners problem, and the unreliable alarm paradigm.

Fuzzy-Systems in Computer Science

Fuzzy control neural fuzzy systems fuzzy systems and artificial intelligence fuzzy classification theoretical aspects of fuzzy systems.

Possibilistic Graphical Models

Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning. which have been well-known for over ten years now. However, they suffer from certain deficiencies, if imprecise information has to be taken into account. Therefore possibilistic graphical modeling has recently emerged as a promising new area of research. Possibilistic networks are a noteworthy alternative to probabilistic networks whenever it is necessary to model both uncertainty and imprecision. Imprecision, understood as set-valued data, has often to be considered in situations in which information is obtained from human observers or imprecise measuring instruments. In this paper we provide an overview on the state of the art of possibilistic networks w.r.t. to propagation and learning algorithms.

Fuzzy control on the basis of equality relations with an example from idle speed control

The way engineers use fuzzy control in real world applications is often not coherent with an understanding of the control rules as logical statements or implications. In most cases fuzzy control can be seen as an interpolation of a partially specified control function in a vague environment, which reflects the indistinguishability of measurements or control values. In this paper the authors show that equality relations turn out to be the natural way to represent such vague environments and they develop suitable interpolation methods to obtain a control function. As a special case of our approach the authors obtain Mamdanis model and can justify the inference mechanism in this model and the use of triangular membership functions not only for the reason of simplified computations, and they can explain why typical fuzzy partitions are preferred. The authors also obtain a criterion for reasonable defuzzification strategies. The fuzzy control methodology introduced in this paper has been applied successfully in a case study of engine idle speed control for the Volkswagen Golf GTI. >

Learning possibilistic networks from data

We introduce the concept of possibilistic learning as a method for structure identification from a database of samples. In comparison to the construction of Bayesian belief networks, the proposed framework has some advantages, namely the explicit consideration of imprecise data, and the realization of a controlled form of information compression in order to increase the efficiency of the learning strategy as well as approximate reasoning using local propagation techniques. Our learning method has been applied to reconstruct a non-singly connected network of 22 nodes and 22 arcs without the need of any a priori supplied node ordering.<<ETX>>

Background and Perspectives of Possibilistic Graphical Models

Graphical modelling is an important tool for the efficient representation and analysis of uncertain information in knowledge-based systems. While Bayesian networks and Markov networks from probabilistic graphical modelling are well-known for a couple of years, the field of possibilistic graphical modelling occurs as a new promising area of research. Possibilistic networks provide an alternative approach compared to probabilistic networks, whenever it is necessary to model uncertainty and imprecision as two different kinds of imperfect information. Imprecision in the sense of set-valued data has often to be considered in situations where data are obtained from human observations or non-precise measurement units. In this contribution we present a comparison of the background and perspectives of probabilistic and possibilistic graphical models, and give an overview on the current state of the art of possibilistic networks with respect to propagation and learning algorithms, applicable to data mining and data fusion problems.

Fuzzy set-theoretic methods in statistics

In this chapter we have gathered some of the approaches which have been introduced in the literature to deal with fuzzy statistical data, as well as some methods to solve inferential (in particular, parameter estimation and hypothesis testing) and decision problems from them.

Parallel Combination of Information Sources

The problem of handling imperfect information has turned out to be a very important issue in the practical use of artificial intelligence for many industrial applications [Luo and Kay, 1995; Pfleger et al., 1993].

A New Approach to Semantic Aspects of Possibilistic Reasoning

The purpose of this paper is to develop a formal environment that provides well-founded semantics of possibilistic reasoning in knowledge-based systems. Representing the universe of discourse as a product space Ω which consists of the domains of a finite number of characterizing attributes, expert knowledge and also evidential knowledge are expected to be given by possibility distributions on subspaces of Ω.

Axiomatic Treatment of Possibilistic Independence

The clarification of the concepts of independence, marginalization, and combination of modularized information is one of the major topics concerning the efficient treatment of imperfect data in complex domains of knowledge. Confining to the uncertainty calculus of possibility theory, we consider a syntactic (based on a set of axioms) as well as a semantic approach (in a random set framework) to appropriate definitions of possibilistic independence. It turns out that well-known, but also new proposals for the concept of possibilistic independence can be justified.