Fundamenta Informaticae

In this paper we present a method of data decomposition to avoid the necessity of reasoning on data with missing attribute values. This method can be applied to any algorithm of classifier induction. The original incomplete data is decomposed into data subsets without missing values. Next, methods for classifier induction are applied to these sets. Finally, a conflict resolving method is used to obtain final classification from partial classifiers. We provide an empirical evaluation of the decomposition method accuracy and model size with use of various decomposition criteria on data with natural missing values. We present also experiments on data with synthetic missing values to examine the properties of proposed method with variable ratio of incompleteness.

A method is proposed to construct decision procedures for various subclasses of first-order logic with equality. We define a notion of complexity of first-order terms and equations, and we propose semantic and syntactic criteria ensuring that existing refinements of the paramodulation calculus terminate on the considered clause sets. These refinements use reduction orderings, selection functions and simplification rules. Since they are sound and refutationally complete, the corresponding classes of formulae are decidable. Moreover, the automatic extraction of models from saturated clause sets is also possible. A discussion and detailed comparisons with existing works in the field are provided, together with numerous examples and some undecidability results.

In this work, we would like to discuss rough inclusions defined in Rough Mereology – a paradigm for approximate reasoning introduced by Polkowski and Skowron [20] – as a basis for common models for rough as well as fuzzy set theories. We would like to adhere to the point of view that tolerance (or, similarity) is the leading motif common to both theories and in this area paths between the two lie. To this end, we demonstrate that rough inclusions (which represent a hierarchy of tolerance relations) induce rough set theoretic approximations as well as partitions and equivalence relations in the sense of fuzzy set theory. For completeness sake, we also discuss granulation mechanisms based on rough inclusions with applications to Rough–Neuro Computing and Computing with Words. These considerations are also carried out in specialized cases of Menger's as well as Łukasiewicz's rough inclusions introduced in the paper.

This paper presents a new model of an artificial neural network solving classification problems, called Local Transfer Function Classifier (LTF-C). Its architecture is very similar to this of the Radial Basis Function neural network (RBF), however it utilizes an entirely different learning algorithm. This algorithm is composed of four main parts: changing positions of reception fields, changing their sizes, insertion of new hidden neurons and removal of unnecessary ones during the training. The paper presents also results of LTF-C application to three real-life tasks: handwritten digit recognition, credit approval and cancer diagnosis. LTF-C was able to solve each of these problems with better accuracy than most popular classification systems. Moreover, LTF-C was relatively small and fast.