Wojciech Ziarko

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.

Variable precision rough set model

Abstract A generalized model of rough sets called variable precision model (VP-model), aimed at modelling classification problems involving uncertain or imprecise information, is presented. The generalized model inherits all basic mathematical properties of the original model introduced by Pawlak. The main concepts are introduced formally and illustrated with simple examples. The application of the model to analysis of knowledge representation systems is also discussed.

Rough Sets, Fuzzy Sets and Knowledge Discovery

An Overview of Knowledge Discovery in Databases: Recent Progress and Challenges.- Rough Sets and Knowledge Discovery: An Overview.- Search for Concepts and Dependencies in Databases.- Rough Sets and Concept Lattices.- Human-Computer Interfaces: DBLEARN and SystemX.- A Heuristic for Evaluating Databases for Knowledge Discovery with DBLEARN.- Knowledge Recognition, Rough Sets, and Formal Concept Lattices.- Quantifying Uncertainty of Knowledge Discovered from Databases.- Temporal Rules Discovery Using Datalogic/R+ with Stock Market Data.- A System Architecture for Database Mining Applications.- An Attribute-Oriented Rough Set Approach for Knowledge Discovery in Databases.- A Rough Set Model for Relational Databases.- Data Filtration: A Rough Set Approach.- Automated Discovery of Empirical Laws in a Science Laboratory.- Hard and Soft Sets.- Rough Set Analysis of Multi-Attribute Decision Problems.- Rough Set Semantics for Non-Classical Logics.- A Note on Categories of Information Systems.- On Rough Sets in Topological Boolean Algebras.- Approximation of Relations.- Variable Precision Rough Sets with Asymmetric Bounds.- Uncertain Reasoning with Interval-Set Algebra.- On a Logic of Information for Reasoning About Knowledge.- Rough Consequence and Rough Algebra.- Formal Description of Rough Sets.- Rough Sets: A Special Case of Interval Structures.- A Pure Logic-Algebraic Analysis of Rough Top and Rough Bottom Equalities.- A Novel Approach to the Minimal Cover Problem.- Algebraic Structures of Rough Sets.- Rough Concept Analysis.- Rough Approximate Operators: Axiomatic Rough Set Theory.- Finding Reducts in Composed Information Systems.- PRIMEROSE: Probabilistic Rule Induction Method Based on Rough Set Theory.- Comparison of Machine Learning and Knowledge Acquisition Methods of Rule Induction Based on Rough Sets.- AQ, Rough Sets, and Matroid Theory.- Rough Classifiers.- A General Two-Stage Approach to Inducing Rules from Examples.- An Incremental Learning Algorithm for Constructing Decision Rules.- Decision Trees for Decision Tables.- Fuzzy Reasoning and Rough Sets.- Fuzzy Representations in Rough Set Approximations.- Trusting an Information Agent.- Handling Various Types of Uncertainty in the Rough Set Approach.- Intelligent Image Filtering Using Rough Sets.- Multilayer Knowledge Base System for Speaker-Independent Recognition of Isolated Words.- Image Segmentation Based on the Indiscernibility Relation.- Accurate Edge Detection Using Rough Sets.- Rough Classification of Pneumonia Patients Using a Clinical Database.- Rough Sets Approach to Analysis of Data of Diagnostic Peritoneal Lavage Applied for Multiple Injuries Patients.- Neural Networks and Rough Sets - Comparison and Combination for Classification of Histological Pictures.- Towards a Parallel Rough Sets Computer.- Learning Conceptual Design Rules: A Rough Sets Approach.- Intelligent Control System Implementation to the Pipe Organ Instrument.- An Implementation of Decomposition Algorithm and its Application in Information Systems Analysis and Logic Synthesis.- ESEP: An Expert System for Environmental Protection.- Author Index.

Rough sets: probabilistic versus deterministic approach

W: B. Gains and J. Boose, editors, Machine Learning and Uncertain Reasoning 3, pages 227-242. Academic Press, New York, NY, 1990. see also: International Journal of Man Machine Studies 29 (1988) 81-85

Generalized vector spaces model in information retrieval

In information retrieval, it is common to model index terms and documents as vectors in a suitably defined vector space. The main difficulty with this approach is that the explicit representation of term vectors is not known a priori. For this reason, the vector space model adopted by Salton for the SMART system treats the terms as a set of orthogonal vectors. In such a model it is often necessary to adopt a separate, corrective procedure to take into account the correlations between terms. In this paper, we propose a systematic method (the generalized vector space model) to compute term correlations directly from automatic indexing scheme. We also demonstrate how such correlations can be included with minimal modification in the existing vector based information retrieval systems. The preliminary experimental results obtained from the new model are very encouraging.

The investigation of the Bayesian rough set model

The original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes.

Probabilistic approach to rough sets

The article introduces the basic ideas and investigates the probabilistic version of rough set theory. It relies on both classification knowledge and probabilistic knowledge in analysis of rules and attributes. Rough approximation evaluative measures and one-way and two-way inter-set dependency measures are proposed and adopted to probabilistic rule evaluation. A new probabilistic dependency measure for attributes is also introduced and proven to have the monotonicity property. This property makes it possible for the measure to be used to optimize and evaluate attribute-based representations through computation of probabilistic measures of attribute reduct, core and significance factors.

DATA‐BASED ACQUISITION AND INCREMENTAL MODIFICATION OF CLASSIFICATION RULES

One of the most important problems in the application of knowledge discovery systems is the identification and subsequent updating of rules. Many applications require that the classification rules be derived from data representing exemplar occurrences of data patterns belonging to different classes. The problem of identifying such rules in data has been researched within the field of machine learning, and more recently in the context of rough set theory and knowledge discovery in databases. In this paper we present an incremental methodology for finding all maximally generalized rules and for adaptive modification of them when new data become available. The methodology is developed in the context of rough set theory and is based on the earlier idea of discernibility matrix introduced by Skowron.

On modeling of information retrieval concepts in vector spaces

The Vector Space Model (VSM) has been adopted in information retrieval as a means of coping with inexact representation of documents and queries, and the resulting difficulties in determining the relevance of a document relative to a given query. The major problem in employing this approach is that the explicit representation of term vectors is not known a priori. Consequently, earlier researchers made the assumption that the vectors corresponding to terms are pairwise orthogonal. Such an assumption is clearly unrealistic. Although attempts have been made to compensate for this assumption by some separate, corrective steps, such methods are ad hoc and, in most cases, formally inconsistent. In this paper, a generalization of the VSM, called the GVSM, is advanced. The developments provide a solution not only for the computation of a measure of similarity (correlation) between terms, but also for the incorporation of these similarities into the retrieval process. The major strength of the GVSM derives from the fact that it is theoretically sound and elegant. Furthermore, experimental evaluation of the model on several test collections indicates that the performance is better than that of the VSM. Experiments have been performed on some variations of the GVSM, and all these results have also been compared to those of the VSM, based on inverse document frequency weighting. These results and some ideas for the efficient implementation of the GVSM are discussed.

Comparison of the probabilistic approximate classification and the fuzzy set model

Abstract It is shown that the generalized notion (probabilistic approximate classification) of rough sets can be conveniently described by the concept of fuzzy sets. A discussion of the proper choice of the definition for the membership function of the intersection (union) of fuzzy sets is also presented. However, from the point of view of the probabilistic approximation space, it is argued that there does not exist a universal definition for the fuzzy intersection (union) operation.