Practical machine learning algorithms are known to degrade in performance (prediction accuracy) when faced with many features (sometimes attribute is used instead of feature) that are not necessary for rule discovery. To cope with this problem, many methods for selecting a subset of features have been proposed. Among such methods, the filter approach that selects a feature subset using a preprocessing step, and the wrapper approach that selects an optimal feature subset from the space of possible subsets of features using the induction algorithm itself as a part of the evaluation function, are two typical ones. Although the filter approach is a faster one, it has some blindness and the performance of induction is not considered. On the other hand, the optimal feature subsets can be obtained by using the wrapper approach, but it is not easy to use because of the complexity of time and space. In this paper, we propose an algorithm which is using rough set theory with greedy heuristics for feature selection. Selecting features is similar to the filter approach, but the evaluation criterion is related to the performance of induction. That is, we select the features that do not damage the performance of induction.

. We recall several applications of Boolean reasoning for feature extraction and we propose an approach based on Boolean reasoning for new feature extraction from data tables with symbolic (nominal, qualitative) attributes. New features are of the form a 2 V , where V ` Va and Va is the set of values of attribute a. We emphasize that Boolean reasoning is also a good framework for complexity analysis of the approximate solutions of the discussed problems. 1 Introduction "Feature Extraction" and "Feature Selection" are important problems in Machine Learning and Data Mining (see e.g. [6, 3, 4]). In previous papers we have considered problems like: short reduct finding problem [16], rule induction problem [17], optimal discretization problem [12], linear feature (hyperplane) searching problem [13]. Our solutions of these problems are based on Boolean reasoning schema [2]. In this paper we discuss a problem of searching for new features from a data table with symbolic (qualitative) value...

This is a continuation of [13]. Let us quote few words from it. "Granulation:::appears:::in di erent names, such as chunking, clustering, data compression, divide and conquer, information hiding, interval computations, and rough set theory, justto name a few. " " the computing theory on information granulation

: We present an approach to the problem of how to learn tolerance relations from decision tables. The tolerance relations constructed (synthesized) in the learning process are applied in the process of extraction of new features which often can be better predisposed than original features (from a given decision table) to the task of the classification of new objects. These tolerances are synthesized from boolean combinations of descriptors and they lead to simpler approximate descriptions of decision classes. The method proposed in the paper extracts tolerance relations encoded in the decision table, contrary to the approach known from literature which consists in taking some a priori fixed tolerance relations and applying them in clustering. Keywords: tolerance relation, feature extraction, decision rules. 1 Introduction A great effort has been made to achieve a progress in clustering methods (see e.g. [2], [6], [9], [11]) and to develop efficient methods for feature extract...

In this paper we present some strategies for synthesis of decision algorithms studied by us. These strategies are used by systems of communicating agents and lead from the original (input) data table to a decision algorithm. The agents are working with parts of data and they compete for the decision algorithm with the best quality of object classification. We give examples of techniques for searching for new features and we discuss some adaptive strategies based on the rough set approach for the construction of a decision algorithm from a data table. We also discuss a strategy of clustering by tolerance. 1.

. The main objective of this chapter is to discuss different approaches to searching for optimal approximation spaces. Basic notions concerning rough set concept based on generalized approximation spaces are presented. Different constructions of approximation spaces are described. The problems of attribute and object selection are discussed. 1 Introduction Rough set theory was proposed [21, 22] as a new approach to processing of incomplete data. Suppose we are given the finite non-empty set U of objects, called the universe. Each object of U is characterized by a description, for example a set of attribute values. In standard rough sets [21, 22] introduced by Pawlak an equivalence relation (reflexive, symmetric and transitive relation) on the universe of objects is defined based on the attribute values. In particular, this equivalence relation is constructed based on the equality relation on attribute values. Many attempts were made to resolve limitations of this approach and many ...

In this paper we consider two related types of data dependencies that can hold in a relation: conjunctive implication rules between attribute-value pairs, and functional dependencies. We present a conceptual clustering approach that can be used, with some small modifications, for inferring a cover for both types of dependencies. The approach consists of two steps. First, a particular clustered representation of the relation, called concept (or Galois) lattice is built; then, a cover is extracted from the lattice built in the earlier step. The main emphasis of this paper is on the second step. We study the computational complexity of the proposed approach and present an experimental comparison with other methods that confirms its validity. The results of the experiments show that our algorithm for extracting implication rules from concept lattices clearly outperforms an earlier algorithm, and suggest that the overall lattice-based approach to inferring functional dependencies from relations can be seen as an alternative to traditional methods.

. Rough set methodology is based on concept (set) approximations constructed from available background knowledge represented in information systems [14]. In many applications only partial knowledge about approximated concepts is given. Hence quite often first a parametrized family of concept approximations is built and next by tuning of the parameters the best, in a sense, approximation is chosen (see e.g. variable precision rough set model [40]) in approximation spaces. In this paper we follow this approach in generalized approximation spaces. We discuss rough set model based on approximation spaces with uncertainty functions and rough inclusions. Both elements of approximation space are parametrized and for the proper application of such model to a particular data set it is necessary to make optimization of the parameters. We discuss basic properties of the mentioned model and also strategies of parameters optimization. We also present different notions of rough relations....

. The present state of rough set theory and its applications is presented by articles in this collection as well as by research papers listed in APPENDIX 1 to which we refer the reader. We would like to discuss here some directions for further research as well as to point to some recent results not mentioned earlier which seem to us to be of importance for development of rough set theory and its applications. In our discussion we will be guided by the following three main topics: (i) Rough Sets in Knowledge Representation; (ii) Rough Sets in Approximate Reasoning about Knowledge; (iii) New Applications and New Hardware/Software. 1 A view on extended rough set theory New applications demand new ideas and their implementations. We would like to point to important new extensions of the nowadays rough set theory. 1.1 Concept Approximation The central theme in our discussion on the lines of the first two topics is that of Concept Approximation. It does involve a description process of ...

The paper presents a method for computing an approximation quality for sorting rules of type "nominal nominal" (NN), "nominal ordinal" (NO), "ordinal ordinal" (OO), and its generalisation to "(nominal, ordinal) ordinal" rules (NO-O). We provide a significance test for the overall approximation quality, and a test for partial influence of attributes based on the bootstrap technology. A competing model is also studied. We show that this method is susceptible to local perturbations in the data set, and dissociated from the theory it claims to support. Key words: Decision support systems, sorting rules, approximation quality, ordinal prediction 1