Rough Set Methods and Applications

In a couple of years that elapsed since the monograph edited by T. Y. Lin and N. Cercone: Rough Sets and Data Mining. Analysis of Imprecise Data (1997) and two monographs edited by L. Polkowski and A. Skowron: Rough Sets in Knowledge Discovery 1, 2 (1998) were presented to the research community (cf. [A]2, [A]3, [A]4 in Bibliography, Appendix 1), rough set researchers have made further progress in inventing methods aimed, among others, at knowledge discovery and data mining, spatial reasoning, data reduction, concurrent system analysis and synthesis, conflict analysis as well as in theoretical analysis of information and decision systems.

The underlying ideas of rough set theory — proposed by Zdzislaw Pawlak in the early 1980’s — have been developed into a manifold theory for the purpose of data and knowledge analysis, due to a systematic growth of interest in this theory in the scientific community, witnessed by — among others — a bibliography of over four hundred research papers on rough sets and their applications produced in the last couple of years and appendiced to this collection of expository papers (in the sequel, we refer to items in this bibliography (see Appendix 1) with indices like [X]xyz where X = A or X = B and xyz is the number of the item in the list X).

We we present some algorithms, based on rough set theory, that can be used for the problem of new cases classification. Most of the algorithms were implemented and included in Rosetta system [43]. We present several methods for computation of decision rules based on reducts. We discuss the problem of real value attribute discretization for increasing the performance of algorithms and quality of decision rules. Finally we deal with a problem of resolving conflicts between decision rules classifying a new case to different categories (classes). Keywords: knowledge discovery, rough sets, classification algorithms, reducts, decision rules, real value attribute discretization

Rough Mereology has been proposed as a paradigm for approximate reasoning in complex information systems [65], [66], [67], [68], [76]. Its primitive notion is that of a rough inclusion functor which gives for any two entities of discourse the degree in which one of them is a part of the other. Rough Mereology may be regarded as an extension of Rough Set Theory as it proposes to argue in terms of similarity relations induced from a rough inclusion instead of reasoning in terms of indiscernibility relations (cf. Chapter 1); it also proposes an extension of Mereology as it replaces the mereological primitive functor of being a part with a more general functor of being a part in a degree. Rough Mereology has deep relations to Fuzzy Set Theory as it proposes to study the properties of partial containment which is also the fundamental subject of study for Fuzzy Set Theory.

The amount of electronic data available is growing very fast and this explosive growth in databases has generated a need for new techniques and tools that can intelligently and automatically extract implicit, previously unknown, hidden and potentially useful information and knowledge from these data. These tools and techniques are the subject of the field of Knowledge Discovery in Databases. In this Chapter we discuss selected rough set based solutions to two main knowledge discovery problems, namely the description problem and the classification (prediction) problem.

Abstract: Knowledge discovery is concerned with extraction of useful information from databases ([21]). One of the basic tasks of knowledge discovery and data mining is to synthesize the description of some subsets (concepts) of entities contained in databases. The patterns and/or rules extracted from data are used as basic tools for concept description. In this Chapter we propose a certain framework for approximating concepts. Our approach emphasizes extracting regularities from data. In this Chapter the following problems are investigated: (1) issues concerning the languages used to represent patterns; (2) computational complexity of problems in approximating concepts; (3) methods of identifying, optimal patterns. Data regularity is a useful tool not only for concept description. It is also indispensable for various applications like classification or decomposition. In this Chapter we present also the applications of data regularity to three basic problems of data mining: classification, data description and data decomposition.

Abstract. In this Chapter rough set methods for the modeling of concurrent processes are considered. The research is motivated by the problems coming from the domains such as, for example: knowledge discovery systems, data mining, control design, decomposition of information systems, object identification in real-time. this Chapter includes, in particular, the description of automatic methods for the modeling and analysis of concurrent systems specified by information systems. In this Chapter the following problems are considered:

Rough set theory, Boolean reasoning, theory of Petri nets as well as self-implemented computer tools are used for this purpose. The methods presented in the paper as well as further investigations of interconnections between rough set theory and concurrency may stimulate the development of both theoretical and practical research related to the areas mentioned above.

Computer support for different human activities has grown up in the latest years. Actually the researchers in Artificial Intelligence benefit from this fact in many fields not considered some years ago. Conflict analysis is one of the fields whose importance is increasing nowadays as distributed systems of computers are starting to play a significant role in the society. The computer aided conflict analysis must be applied when intelligent machines (agents) interact. However this is only one from many different areas where a conflict can arise like business, government, political or military operations, labour-management negotiations etc.etc.

Abstract. In this paper, we shall give an introduction to, and an overview of, the various relational, algebraic, and logical tools that are available to handle rule based reasoning.

Concept forming and classification in the absence of complete or certain information has been a major concern of artificial intelligence for some time. Traditional “hard” data analysis based on statistical models or are in many cases not equipped to deal with uncertainty, relativity, or non—monotonic processes. Even the recently popular “soft” computing approach with its principal components “... fuzzy logic, neural network theory, and probabilistic reasoning” [16] uses quite hard parameters outside the observed phenomena, e.g. representation and distribution assumptions, prior probabilities, beliefs, or membership degrees, the origin of which is not always clear; one should not forget that the results of these methods are only valid up to the — stated or unstated — model assumptions. The question arises, whether there is a step in the modelling process which is informative for the researcher and, at the same time, does not require additional assumptions about the data. To make this clearer, we follow [9] in assuming that a data model consists of

Basic ideas of rough set theory were proposed by Zdzislaw Pawlak [90, 91] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world-wide growth of interest in rough sets and their applications. There are numerous areas of successful applications of rough set software systems [101]. Many interesting case studies are reported (for references see e.g., [100, 101], [87] and the bibliography in these books, in particular [19], [46], [57], [132], [1461).

The main goal of rough set analysis is induction of approximations of concepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete with respect to expressibility. A fortiori, we have to describe concepts of interest (features, properties, relations etc.) known not completely but by means of their reflections (i.e., approximations) in the chosen language. The most important issues in this induction process are:

Basic tools of rough set approach are related to concept approximations. They are defined by approximation spaces. For many applications, in particular for KDD problems, it is necessary to search for relevant approximation spaces in the large space of parameterized approximation spaces. Strategies for tuning parameters of approximation spaces are crucial for inducing concept approximations of high quality.

Methods proposed in rough set approach are kin to general methods used to solve Knowledge Discovery and Data Mining (KDD) problems like feature selection, feature extraction (e.g., discretization or grouping of symbolic value), data reduction, decision rule generation, pattern extraction (templates, association rules), or decomposition of large data tables. In this Chapter we examine rough set contributions to Knowledge Discovery from the perspective of KDD as a whole.

This Chapter shows how several aspects of the above problems are solved by the classical rough set approach and how they are approached by some recent extensions to the classical theory of rough sets. We point out the role of Boolean reasoning in solving discussed problems. Rough sets induce via its methods a specific logic, which we call rough logic. We also discuss rough logic and related logics from a wider perspective of logical approach in KDD. We show some relationships between these logics and potential directions for further research on rough logic.