Jerzy W. Grzymala-Busse

Rough sets

Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.

LERS-A System for Learning from Examples Based on Rough Sets

The paper presents the system LERS for rule induction. The system handles inconsistencies in the input data due to its usage of rough set theory principle. Rough set theory is especially well suited to deal with inconsistencies. In this approach, inconsistencies are not corrected. Instead, system LERS computes lower and upper approximations of each concept. Then it induces certain rules and possible rules. The user has the choice to use the machine learning approach or the knowledge acquisition approach. In the first case, the system induces a single minimal discriminant description for each concept. In the second case, the system induces all rules, each in the minimal form, that can be induced from the input data. In both cases, the user has a choice between the local or global approach.

A new version of the rule induction system LERS

A new version of the rule induction system LERS is described and compared with the old version of LERS. Experiments were done for comparison of performance for both versions of LERS and the two other rule-induction systems: AQ15 and C4.5. The new LERS system performance is fully comparable with performance of the other two systems.

A Comparison of Several Approaches to Missing Attribute Values in Data Mining

In the paper nine different approaches to missing attribute values are presented and compared. Ten input data files were used to investigate the performance of the nine methods to deal with missing attribute values. For testing both naive classification and new classification techniques of LERS (Learning from Examples based on Rough Sets) were used. The quality criterion was the average error rate achieved by ten-fold cross-validation. Using the Wilcoxon matched-pairs signed rank test, we conclude that the C4.5 approach and the method of ignoring examples with missing attribute values are the best methods among all nine approaches; the most common attribute-value method is the worst method among all nine approaches; while some methods do not differ from other methods significantly. The method of assigning to the missing attribute value all possible values of the attribute and the method of assigning to the missing attribute value all possible values of the attribute restricted to the same concept are excellent approaches based on our limited experimental results. However we do not have enough evidence to support the claim that these approaches are superior.

Global Discretization of Continuous Attributes as Preprocessing for Machine Learning

Abstract Real-life data usually are presented in databases by real numbers. On the other hand, most inductive learning methods require a small number of attribute values. Thus it is necessary to convert input data sets with continuous attributes into input data sets with discrete attributes. Methods of discretization restricted to single continuous attributes will be called local, while methods that simultaneously convert all continuous attributes will be called global. In this paper, a method of transforming any local discretization method into a global one is presented. A global discretization method, based on cluster analysis, is presented and compared experimentally with three known local methods, transformed into global. Experiments include tenfold cross-validation and leaving-one-out methods for ten real-life data sets.

Knowledge Acquisition under Uncertainty- a Rough Set Approach

The paper describes knowledge acquisition under uncertainty using rough set theory, a concept introduced by Z. Pawlak in 1981. A collection of rules is acquired, on the basis of information stored in a data base-like system, called an information system. Uncertainty implies inconsistencies, which are taken into account, so that the produced rules are categorized into certain and possible with the help of rough set theory. The approach presented belongs to the class of methods of learning from examples. The taxonomy of all possible expert classifications, based on rough set theory, is also established. It is shown that some classifications are theoretically (and, therefore, in practice) forbidden.

Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction

Data sets, described by decision tables, are incomplete when for some cases (examples, objects) the corresponding attribute values are missing, e.g., are lost or represent “do not care” conditions. This paper shows an extremely useful technique to work with incomplete decision tables using a block of an attribute-value pair. Incomplete decision tables are described by characteristic relations in the same way complete decision tables are described by indiscernibility relations. These characteristic relations are conveniently determined by blocks of attribute-value pairs. Three different kinds of lower and upper approximations for incomplete decision tables may be easily computed from characteristic relations. All three definitions are reduced to the same definition of the indiscernibility relation when the decision table is complete. This paper shows how to induce certain and possible rules for incomplete decision tables using MLEM2, an outgrow of the rule induction algorithm LEM2, again, using blocks of attribute-value pairs. Additionally, the MLEM2 may induce rules from incomplete decision tables with numerical attributes as well.

Transactions on Rough sets I

Rough Sets - Introduction.- Some Issues on Rough Sets.- Rough Sets - Theory.- Learning Rules from Very Large Databases Using Rough Multisets.- Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction.- Generalizations of Rough Sets and Rule Extraction.- Towards Scalable Algorithms for Discovering Rough Set Reducts.- Variable Precision Fuzzy Rough Sets.- Greedy Algorithm of Decision Tree Construction for Real Data Tables.- Consistency Measures for Conflict Profiles.- Layered Learning for Concept Synthesis.- Basic Algorithms and Tools for Rough Non-deterministic Information Analysis.- A Partition Model of Granular Computing.- Rough Sets - Applications.- Musical Phrase Representation and Recognition by Means of Neural Networks and Rough Sets.- Processing of Musical Metadata Employing Pawlaks Flow Graphs.- Data Decomposition and Decision Rule Joining for Classification of Data with Missing Values.- Rough Sets and Relational Learning.- Approximation Space for Software Models.- Application of Rough Sets to Environmental Engineering Models.- Rough Set Theory and Decision Rules in Data Analysis of Breast Cancer Patients.- Independent Component Analysis, Principal Component Analysis and Rough Sets in Face Recognition.

On the Unknown Attribute Values in Learning from Examples

In machine learning many real-life applications data are characterized by attributes with unknown values. This paper shows that the existing approaches to learning from such examples are not sufficient. A new method is suggested, which transforms the original decision table with unknown values into a new decision table in which every attribute value is known. Such a new table, in general, is inconsistent. This problem is solved by a technique of learning from inconsistent examples, based on rough set theory. Thus, two sets of rules: certain and possible are induced. Certain rules are categorical, while possible rules are supported by existing data, although conflicting data may exist as well. The presented approach may be combined with any other approach to uncertainty when processing of possible rules is concerned.

Three discretization methods for rule induction

We discuss problems associated with induction of decision rules from data with numerical attributes. Real‐life data frequently contain numerical attributes. Rule induction from numerical data requires an additional step called discretization. In this step numerical values are converted into intervals. Most existing discretization methods are used before rule induction, as a part of data preprocessing. Some methods discretize numerical attributes while learning decision rules. We compare the classification accuracy of a discretization method based on conditional entropy, applied before rule induction, with two newly proposed methods, incorporated directly into the rule induction algorithm LEM2, where discretization and rule induction are performed at the same time. In all three approaches the same system is used for classification of new, unseen data. As a result, we conclude that an error rate for all three methods does not show significant difference, however, rules induced by the two new methods are simpler and stronger. © 2001 John Wiley & Sons, Inc.