A. de Korvin

On interval weighted three-layer neural networks

When solving application problems, the data sets used to train a neural network may not be one hundred percent precise but are within a certain range. By representing data sets with intervals, one has interval neural networks. By analyzing the mathematical model, the authors categorize general three-layer neural network training problems into two types. One of them can be solved by finding numerical solutions of nonlinear systems of equations. The other can be transformed into nonlinear optimization problems. Reliable interval algorithms such as interval Newton/generalized bisection method and interval branch-and-bound algorithm are applied to obtain optimal weights for interval neural networks. Applicable state-of-art interval software packages are also reviewed.

Analysis by fuzzy difference equations of a model of CO2 level in the blood

In this paper we shall consider a model to determine the carbon dioxide (CO2) level in the blood. The model consists of a set of nonlinear difference equations. However, the linearized model will be solved. Since many measurements and factors that determine the CO2 level in the blood may be imprecise, we will consider the fuzzy analog of the linearized model as a method to compensate for these imprecise measurements. We will estimate, for a fixed threshold α, a solution to the fuzzy difference equation with belief at least α. We will show that the results reduce to the classical case when the fuzzy quantities are replaced by crisp ones.

Object Identification When Imprecise Information is Available from Multiple Sources of Unequal Reliability

In this article we consider the problem of object identification when there is imprecise and perhaps conflicting information from information sources of unequal reliability. Data is represented by fuzzy sets, and the decision set in which the value of this imprecise information is modified by its importance in the context of the specific problem at hand is a type II fuzzy set in which the memberships are themselves fuzzy sets. Three criteria are proposed for making the classification based on the information contained in this type II fuzzy set. A simple example illustrates the procedure.

Extracting Fuzzy Rules Under Uncertainty and Measuring Definability Using Rough Sets

In this article we consider attributes to be fuzzy sets. Knowledge acquisition takes place by looking at examples. In each example, attributes as well as a corresponding decision is made available. The decision may be a fuzzy diagnosis. Based on these examples two sets of fuzzy rules are constructed: certain rules and possible rules. Corresponding measures of how much we believe these rules are also constructed. The concept of how much a fuzzy diagnosis is definable in terms of fuzzy attributes is studied. Finally, classifications and some of their properties are analyzed.

An Approach to Object Identification Using Fuzzy Expected Payoffs

Imprecise information regarding feature values of an unidentified object is obtained from information sources of varying reliability. This imprecise information is used to construct a fuzzy probability distribution over the set of environments, which consist of all possible combinations of feature values. A fuzzy payoff matrix is constructed in which the rows represent all possible objects and the columns represent all possible environments. A fuzzy expected payoff is computed for each object i.e., row in this matrix. Each fuzzy expected payoff is then intersected with a maximizing set, and the object is identified as the one for which this intersection has the highest percentage of optimal values according to a specific criterion.

The object recognition problem when features fail to be homogeneous

Abstract The goal of the present work is to obtain a reasonable solution to the problem of object identification. Sensors report on certain independent feature values of an object. The Dempster-Shafer theory is used to integrate the information coming from these independent sources. Moreover, the sensors do not report the feature values in a crisp manner. These values are only stochastically determined. Also, in the data base itself, objects only partially belong to classes determined by feature views. This might be due to the inability of the expert or expert system to pinpoint exactly the feature value of a given object. This setting naturally leads to applying the Dempster-Shafer theory to masses whose focal elements are fuzzy sets. A similar approach is taken to produce an economical solution to the problem of object identification. A set of sensors is picked based on performance evaluation.

A belief function approach to information utilization in decision making

A model for decision making is proposed which is based on an elimination process utilizing sequentially acquired information. The procedure combines aspects of the belief‐plausibility approach developed by Shafer and the generalized information system proposed by Yovits, et al. Although based on formalized rules and mathematical structures, the approach taken is basically the method used by many human decision makers when confronted with a major decision. An extensive example illustrates the technique.

An evidential approach to problem solving when a large number of knowledge systems is available

Many problems deal with knowledge and information itself and can be generalized beyond the specialized areas of expertise from which they originate. A powerful method in artificial intelligence is to look at certain features of a problem and to combine the evidence so obtained in order to perceive a general pattern. This article describes a paradigm in which the Dempster‐Shafer method of combining evidence from independent sources is used for two distinct, but closely related purposes. the first of these is to obtain the answer to a specific query, while the second is to define a dynamic policy for parallel accessing of relevant knowledge systems. the access policy is determined by a sequence of goals which are themselves subdivided into control characteristics of potential knowledge systems. This article concentrates on the general approach and fundamental mathematics involved in this procedure. Specific applications will be dealt with in future research.

Project management: using fuzzy logic and the Dempster-Shafer theory of evidence to select team members for the project duration

Fuzzy logic and the Dempster-Shafer theory of evidence is applied to an IS multiattribute decision making problem whereby the project manager must select project team members from candidates, none of whom may exactly satisfy the ideal level of skills needed at any point in time. The decision mechanism is constrained by the uncertainty inherent in the determination of the relative importance of each skill and the classification of potential team members. This latter uncertainty of potential team membership is addressed through expert evaluation of the degree to which each potential ream member possesses each skill. Then the belief and plausibility that a candidate will satisfy the decision makers ideal skill levels are calculated and combined to rank order the available candidates. The changing skill requirements are addressed through an iterative process for each project phase.

Transition probabilities for Markov chains having fuzzy states

We consider a Markov Chain in which the states are fuzzy subsets defined on some finite state space. Building on the relationship between set-valued Markov chains to the Dempster-Shafer combination rule, we construct a procedure for finding transition probabilities from one fuzzy state to another. This construction involves Dempster-Shafer type mass functions having fuzzy focal elements. It also involves a measure of the degree to which two fuzzy sets are equal. We also show how to find approximate transition probabilities from a fuzzy state to a crisp state in the original state space