International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In the sequel, we shall be concerned with the automated induction of prototypes to represent a database in a way that combines transparency and accuracy. More precisely, our aim is to automatically summarize the information from a set of data using prototypes and simultaneously decide on the number of prototypes needed to the represent the data adequately. We propose to use fuzzy prototypes, which correspond to groupings of similar objects represented by tuples of fuzzy sets over attribute universes. In the case of numerical attributes, the universes will be discretized using linguistic variables and the attribute values will be described by fuzzy sets on words. To learn the prototypes, we shall present an algorithm inspired by hierarchical clustering techniques, which makes use of new measures of prototype similarity and of prototype addition. Also, a pruning algorithm will be incorporated which uses a new heuristic measure of prototype quality to fuse overly specific prototypes. The potential of the resulting method will be illustrated by its application to a number of classification problems and comparing its performance with that of previous approaches in the literature.

This paper describes a domain independent approach for automatically constructing information extraction patterns for semi-structured web pages. Given a randomly chosen page from a web site of similarly structured pages, the system identifies a region of the page that has a regular "tabular" structure, and then infers an extraction pattern that will match the "rows" of the region and identify the data elements. The approach was tested on three corpora containing a series of tabular web sites from different domains and achieved a success rate of at least 80%. A significant strength of the system is that it can infer extraction patterns from a single training page and does not require any manual labeling of the training page.

The main goal of this paper is to develop such means of analysis that allows us to reflect and model vagueness and uncertainty of our knowledge, which result from imprecision of measurement and inaccuracy of computation. To achieve this goal, we use here neoclassical analysis to problems of optimization. Neoclassical analysis extends the scope and results of the classical mathematical analysis by applying fuzzy concepts to conventional mathematical objects, such as functions, sequences, and derivatives. Basing on the theory of fuzzy limits, we construct a fuzzy extension for the classical theory of differentiation in the context of computational mathematics. It is done in the second part of this paper, going after introduction. Two kinds of fuzzy derivatives of real functions are considered: weak and strong ones. In addition, we introduce and study extended fuzzy derivatives, which may take infinite values. In the third part of this paper, fuzzy derivatives are applied to a study of maxima and minima of real functions. Different conditions for maxima and minima of real functions are obtained. Some of them are the same or at least similar to the conditions for the differentiable functions, while others differ in many aspects from those for the standard differentiable functions. Many classical results are obtained as direct corollaries of propositions for fuzzy derivatives, which are proved in this paper. Such results as the Fuzzy Intermediate Value theorem, Fuzzy Fermat's theorem, Fuzzy Rolle's theorem, and Fuzzy Mean Value theorem are proved. These results provide better theoretical base for computational methods of optimization.

We consider the interval ]-1, 1[ and intend to endow it with an algebraic structure like a ring. The motivation lies in decision making, where scales that are symmetric w.r.t. 0 are needed in order to represent a kind of symmetry in the behaviour of the decision maker. A former proposal due to Grabisch was based on maximum and minimum. In this paper, we propose to build our structure on t-conorms and t-norms, and we relate this construction to uninorms. We show that the only way to build a group is to use strict t-norms, and that there is no way to build a ring. Lastly, we show that the main result of this paper is connected to the theory of ordered Abelian groups.

It is well known that an intuitionistic fuzzy relation is a generalization of a fuzzy relation. In fact there are situations where intuitionistic fuzzy relations are more appropriate. This paper discusses the fuzzy clustering based on intuitionistic fuzzy relations. On the basis of max-t & min-s compositions, we discuss an n-step procedure which is an extension of Yang and Shih's [17] n-step procedure. A similarity-relation matrix is obtained by beginning with a proximity-relation matrix using the proposed n-step procedure. Then we propose a clustering algorithm for the similarity-relation matrix. Numerical comparisons of three critical max-t & min-s compositions: max-t₁ & min-s₁, max-t₂ & min-s₂ and max-t₃ & min-s₃, are made. The results show that max-t₁ & min-s₁ compositions has better performance. Sometimes, data may be missed with an incomplete proximity-relation matrix. Imputation is a general and flexible method for handling missing-data problem. In this paper we also discuss a simple form of imputation is to estimate missing values by max-t & min-s compositions.

We extend previous work regarding the transitivity of fuzzy matrices and propose the concept of completely transitive matrices. We further investigate their properties, indices, periods and relations with canonical fuzzy matrices. Our research shows that the completely transitive matrix type is a novel type, which contains previously defined transitive matrix types. Based on the proposed theories, we illustrate that completely transitive matrices can be applied in fuzzy orderings.

In this paper, we present the definition of integral of fuzzy mappings from the fuzzy number space E into E, and discuss its properties and calculation. And as an application of the integral, we provide a method of robustness estimates for the traffic volumes passing a road each day (24 hours). In addition, we also give another example of the integral characterizing the distance travelled in an imprecise or uncertain environment of time and speed.

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@cs.utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.