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3rd International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU '90 Paris, France, July 2–6, 1990 Proceedings
This paper is about Spohn's theory of epistemic beliefs. The main ingredients of Spohn's theory are (i) a functional representation of an epistemic state called a disbelief function, and (ii) a rule for revising this function in light of new information. The main contribution of this paper is as follows. First, we provide a new axiomatic definition of an epistemic state and study some of its properties...
The runtime of the usual algorithms computing the transformation of a basic belief assignment into its associated belief function and conversely is an exponential function of the cardinality of (the domain of) the basic belief assignment. In this paper, new algorithms with a polynomial runtime are presented. These algorithms appear to be optimal in the class of the so-called M-algorithms.
Subject of this paper is a thorough modeling of uncertain knowledge based on the theory of belief functions. In this context it has to be taken into account, that some experts state of mind changes in the light of new information, thus we introduce the notion of an information source. Considering the integration of information sources it turns out that this approach leads to Dempster's well-known...
Axiomatic properties of qualitative conditional independence are compared to those of a Bayesian belief network approach, and judged as to their applicational relevance. It is found that qualitative conditional independence uses weaker axioms and has a clear interpretation in terms of the algebra of non-first normal form relations, and that it can be extended to the recently defined conditional event...
This paper compares the expressions obtained from an analysis of a problem involving conflicting evidence when using Dempster's rule of combination and conditional probabilities. Several results are obtained showing if and when the two methodologies produce the same results. The role played by the normalizing constant is shown to be tied to prior probability of the hypothesis if equality is to occur...
Constraint systems as used in temporal reasoning usually describe uncertainty by constraining variables into given sets. Viewing belief functions as random or uncertain sets, uncertainty in such models is quite naturally and more generally described by belief functions. Here a special class of constraint systems induced by the additive underlying group structure is considered. Belief functions are...
In this paper, it is considered the concept of conditioning for a family of possible probability distributions. First, the most used definitions are reviewed, in particular, Dempster conditioning, and upper-lower probabilities conditioning. It is shown that the former has a tendency to be too informative, and the last, by the contrary, too uninformative. Another definitions are also considered, as...
Dempster's rule of combination, the main inference mechanism of the Dempster-Shafer theory of belief functions [Shafer 76; Smets 88], requires that the belief functions to be combined must be "independent". This independence assumption is usually understood to be composed of two parts: (1) the uniqueness assumption, which states that each belief function to be combined is based on a unique...
We present an algorithm that is able to integrate uncertain probability statements of different default levels. In case of conflict between statements of different levels the statements of the lower levels are ignored. The approach is applicable to inference networks of arbitrary structure including loops and cycles. The simulated annealing algorithm may be used to derive a distribution which best...
Three focal elements of knowledge-based system design are (i) acquiring information from an expert, (ii) representing the information in a system-usable form, and (iii) using the information to draw inferences about specific problem instances. In the artificial intelligence (AI) literature, the first element is referred to as knowledge acquisition, while the second and third are embodied in a system's...
This paper describes a computational system, called STOSS (STOchastic Simulation System), using the stochastic simulation method to perform probabilistic reasoning for Bayesian belief networks. The system is then applied to an artificial example in the field of forensic science and the results are compared with the calculations obtained using the Causal Probabilistic Reasoning System (CPRS).
Ad hoc techniques and inference methods used in expert systems are often logically inconsistent. On the other hand, among properties and assertions concerning handling of uncertainty, those which turns out to be well founded can be in general easily deduced from probability laws. Relying on the general concept of event as a proposition and starting from a few conditional events of initial...
Developers of artificial intelligence-based systems have made frequent use of likelihood ratios. Those ratios have been used to represent the uncertainty associated with events and hypotheses on rules in expert systems and they have been used to establish rankings of resulting diagnoses in other systems. This paper discusses the representation of source reliability through those likelihood ratios,...
Fril is an AI language incorporating a powerful mechanism for handling uncertainty in knowledge-based applications. It is implemented as a compiler producing code for an abstract machine. In this paper, we outline the features of the abstract machine used to handle uncertainty and illustrate their operation by reference to a simple example.
During the last years, the development of knowledge based systems has taken an increasing expansion in the control of complex industrial processes. The control knowledge is often vague, and it is necessary to create a tool to define the words of the language that are used by the expert when this one is reasoning. We propose a method to acquire and to represent the vague knowledge of the expert. ...
First, this paper investigates a model of the database with fuzzy information and generalizes a class of fuzzy indiscernibility relations from the model. Next, this paper is focused on algebraic analysis of the fuzzy indiscernibility, i.e., defining an algebraic structure based on the fuzzy indiscernibility; showing the representation theorem and the center of a given algebra.
A theory of a fuzzy weak preference relation based on multiple-valued logic is developed. The transitivity property of fuzzy strict preference and indifference relations associated with a fuzzy weak preference relation is established.
In this paper we present a set of tools to analyze concepts that describe and explain a set of observations. Due to the inherent vagueness of concepts, that makes hard to decide in a dichotomic base weather an observation is, or is not, a good example for a concept, we consider the concepts associated to fuzzy subsets. Then we study the adequation and coverage of a collection of fuzzy sets to describe...
The set of solutions of relational equations over a finite referential space and with values from a linear lattice is considered. We determine in this set the greatest max-min transitive solution and the related minimal ones. Further, we investigate for the determination of particular max-min transitive solutions, namely those having Schein rank equal to 1. Related properties of convergence of fuzzy...
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