Showing papers on "Rough set published in 1998"
TL;DR: This work proposes reduction of knowledge that eliminates only that information, which is not essential from the point of view of classification or decision making, and shows how to find decision rules directly from such an incomplete decision table.
1,239 citations
01 Jan 1998
1,139 citations
TL;DR: This paper presents a framework for the formulation, interpretation, and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations, and introduces a special class of neighborhood system, called 1-neighborhood systems.
967 citations
TL;DR: This paper reviews and compares constructive and algebraic approaches in the study of rough set algebras and states axioms that must be satisfied by the operators.
772 citations
TL;DR: The lower and upper approximation of a set, the basic operations of the theory, are intuitively explained and formally defined.
Abstract: This paper gives basic ideas of rough set theory a new approach to data analysis The lower and upper approximation of a set, the basic operations of the theory, are intuitively explained and formally defined Some applications of rough set theory are briefly outlined and some future problems are outlined
754 citations
TL;DR: The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension, which makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets.
567 citations
Book•
31 Aug 1998TL;DR: This chapter discusses data mining and knowledge discovery through the lens of machine learning, and some of the techniques used in this chapter were previously described in the preface.
Abstract: Foreword. Preface. 1. Data Mining and Knowledge Discovery. 2. Rough Sets. 3. Fuzzy Sets. 4. Bayesian Methods. 5. Evolutionary Computing. 6. Machine Learning. 7. Neural Networks. 8. Clustering. 9. Preprocessing. Index.
552 citations
TL;DR: This work presents three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle, based on the principle of indifference combined with the maximum entropy principle, thus keeping external model assumptions to a minimum.
403 citations
01 Feb 1998
TL;DR: A new concept of shadowed sets is introduced that can be regarded as a certain operational framework simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein.
Abstract: This study introduces a new concept of shadowed sets that can be regarded as a certain operational framework simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein. Some conceptual links between this idea and some others known in the literature are established. In particular, it is demonstrated how fuzzy sets can induce shadowed sets. Subsequently, shadowed sets reveal interesting conceptual and algorithmic relationships existing between rough sets and fuzzy sets. Detailed computational aspects of shadowed sets are discussed. Several illustrative examples are provided.
371 citations
TL;DR: This paper reviews and compares theories of fuzzy sets and rough sets, and two approaches for the formulation of fuzzy set are reviewed, one is based on many-valued logic and the other isbased on modal logic.
Book•
01 Jan 1998
TL;DR: This book discusses Rough Sets as a Methodology for Data Mining, the Design and Implementation of a Knowledge Discovery Toolkit Based on Rough Sets - The ROSETTA System, and methods and applications.
Abstract: Z. Pawlak: Foreword.- Introduction: L. Polkowski, A. Skowron: Introducing the Book Z. Pawlak: Rough Set Elements L. Polkowski, A. Skowron: Rough Sets: A Perspective.- Foundations: G. Cattaneo: Abstract Approximation Spaces for Rough Theories S. Demri, E. Orlowska: Complementarity Relations: Reduction of Decision Rules and Informational Representability T.Y. Lin: Granular Computing on Binary Relations I. Data Mining and Neighborhood Systems T.Y. Lin: Granular Computing II. Rough Set Representations and Belief Functions S. Miyamaoto: Fuzzy Multisets and a Rough Approximation by Multiset-Valued Function M. Moshkov: On Time Complexity of Decision Trees A. Nakamura: Graded Modalities in Rough Logic P. Pagliani: A Practical Introduction to the Model-Relational Approach to Approximation Spaces E. SanJuan, L. Iturrioz: Duality and Information Representability of some Information Algebras J. Stepaniuk: Rough Relations and Logics A. Wasilewska, L. Vigneron: Rough Algebras and Automated Deduction S.K.M. Wong: A Rough-Set Model for Reasoning about Knowledge Y.Y. Yao: Generalized Rough Set Models.- Methods and Applications: J.G. Bazan: A Comparison of Dynamic and Non-Dynamic Rough Set Methods for Extracting Laws from Decision Tables J.W. Grzymala-Busse: Applications of the Rule Induction Systems LERS A. Ohrn, J. Komorowski, A. Skowron, P. Synak: The Design and Implementation of a Knowledge Discovery Toolkit Based on Rough Sets - The ROSETTA System W. Kowalczyk: Rough Data Modelling: a New Technique for Analyzing Data M. Kryszkiewicz: Properties of Incomplete Information Systems in the Framework of Rough Sets H. Son Nguyen, S. Hoa Nguyen: Discretization Methods in Data Mining Z. Piasta, A. Lenarcik: Learning Rough Classifiers from Large Databases with Missing Values J. Stefanowski: On Rough Set Based Approaches to Induction of Decision Rules R. Susmaga: Experiments in Incremental Computation of Reducts W. Ziarko: Rough Sets as a Methodology for Data Mining.
TL;DR: A rule induction method is introduced, which extracts not only classification rules but also other medical knowledge needed for diagnosis from clinical cases, and is evaluated on three clinical databases.
TL;DR: This paper addresses the measurement of uncertainty in rough sets and rough relational databases by introducing a measurement based on information theory, and rough entropy is discussed as it applies to rough sets in general and in particular to aspects of the rough relational database model.
04 May 1998
TL;DR: Basic concepts of rough set theory are defined and their granular structure pointed out and the consequences of granularity of knowledge for reasoning about imprecise concepts are discussed.
Abstract: Granularity of knowledge has attracted attention of many researchers. This paper concerns this issue from the rough set perspective. Granularity is inherently connected with the foundation of rough set theory. The concept of the rough set hinges on classification of objects of interest into similarity classes, which form elementary building blocks (atoms, granules) of knowledge. These granules are employed to define basic concepts of the theory. In the paper basic concepts of rough set theory are defined and their granular structure pointed out. Next the consequences of granularity of knowledge for reasoning about imprecise concepts are discussed.
01 Jan 1998
TL;DR: This approach is based on approximations of a given partition of a set of firms into pre-defined and ordered categories of risk by means of dominance relations, instead of indiscernibility relations, which maintains the best properties of the original rough set analysis.
Abstract: We present a new rough set method for evaluation of bankruptcy risk. This approach is based on approximations of a given partition of a set of firms into pre-defined and ordered categories of risk by means of dominance relations, instead of indiscernibility relations. This type of approximations enables us to take into account the ordinal properties of considered evaluation criteria. The new approach maintains the best properties of the original rough set analysis: it analyses only facts hidden in data, without requiring any additional information, and possible inconsistencies are not corrected. Moreover, the results obtained in terms of sorting rules are more understandable for the user than the rules obtained by the original approach, due to the possibility of dealing with ordered domains of criteria instead of non-ordered domains of attributes. The rules based on dominance are also better adapted to sort new actions than the rules based on indiscernibility. One real application illustrates the new approach and shows its advantages with respect to the original rough set analysis.
TL;DR: Computational methods for the rough analysis of databases, a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty, are discussed.
Book•
01 Oct 1998
TL;DR: When you need to find rough sets in knowledge discovery 2 applications case studies and software systems, the following book can be a great choice.
Abstract: Many people are trying to be smarter every day. How's about you? There are many ways to evoke this case you can find knowledge and lesson everywhere you want. However, it will involve you to get what call as the preferred thing. When you need this kind of sources, the following book can be a great choice. rough sets in knowledge discovery 2 applications case studies and software systems is the PDF of the book.
TL;DR: A method for updating approximations of a concept incrementally is presented, using the inductive learning algorithm, LERS based on rough set theory, to implement a quasi-incremental algorithm for learning classification rules from very large data bases generalized by dynamic conceptual hierarchies provided by users.
04 May 1998
TL;DR: This work addresses the problem of synthesis of adaptive decision algorithms and proposes an approach based on the notion of a granule which is developed in the framework of rough mereology, which does encompass both rough and fuzzy set theories.
Abstract: An importance of the idea of granularity of knowledge for approximate reasoning has been stressed in Pawlak (1997) and Zadeh (1966, 1997). We address here the problem of synthesis of adaptive decision algorithms and we propose an approach to this problem based on the notion of a granule which we develop in the framework of rough mereology. This framework does encompass both rough and fuzzy set theories. Our approach may be applied in the problems of approximate synthesis of complex objects (solutions) in distributed systems of intelligent agents.
TL;DR: This paper reviews and discusses generalizations of Pawlak rough set approximation operators in mathematical systems, such as topological spaces, closure systems, lattices, and posets.
Abstract: This paper reviews and discusses generalizations of Pawlak rough set approximation operators in mathematical systems, such as topological spaces, closure systems, lattices, and posets. The structures of generalized approximation spaces and the properties of approximation operators are analyzed.
TL;DR: ROSE software package is an interactive, modular system designed for analysis and knowledge discovery based on rough set theory in 32-bit operating systems on PC computers that includes generation of decision rules for classification systems and knowledgeiscovery.
Abstract: This paper briefly describes ROSE software package. It is an interactive, modular system designed for analysis and knowledge discovery based on rough set theory in 32-bit operating systems on PC computers. It implements classical rough set theory as well as its extension based on variable precision model. It includes generation of decision rules for classification systems and knowledge discovery.
01 Jan 1998
TL;DR: This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe and considers the notion of interval algebras, which may be used to interpret any belief functions.
Abstract: This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe. The concept of standard rough set algebras is generalized in two directions. One is based on the use of nonequivalence relations. The other is based on relations over two universes, which leads to the notion of interval algebras. Pawlak rough set algebras may be used to interpret belief functions whose focal elements form a partition of the universe. Generalized rough set algebras using nonequivalence relations may be used to interpret belief functions which have less than | U | focal elements, where | U | is the cardinality of the universe U on which belief functions are defined. Interval algebras may be used to interpret any belief functions.
TL;DR: A new scheme of knowledge encoding in a fuzzy multilayer perceptron (MLP) using rough set-theoretic concepts is described, demonstrating the superiority of the system over the fuzzy and conventional versions of the MLP (involving no initial knowledge).
Abstract: A scheme of knowledge encoding in a fuzzy multilayer perceptron (MLP) using rough set-theoretic concepts is described. Crude domain knowledge is extracted from the data set in the form of rules. The syntax of these rules automatically determines the appropriate number of hidden nodes while the dependency factors are used in the initial weight encoding. The network is then refined during training. Results on classification of speech and synthetic data demonstrate the superiority of the system over the fuzzy and conventional versions of the MLP (involving no initial knowledge).
15 Apr 1998
TL;DR: It is demonstrated that a generalized rough set model can be used for generating rules from incomplete databases and these rules are based on plausibility functions proposed by Shafer.
Abstract: This article examines basic issues of data mining using the theory of rough sets, which is a recent proposal for generalizing classical set theory. The Pawlak rough set model is based on the concept of an equivalence relation. Recent research has shown that a generalized rough set model need not be based on equivalence relation axioms. The Pawlak rough set model has been used for deriving deterministic as well as probabilistic rules from a complete database. This article demonstrates that a generalized rough set model can be used for generating rules from incomplete databases. These rules are based on plausibility functions proposed by Shafer. The article also discusses the importance of rule extraction from incomplete databases in data mining. © 1998 John Wiley & Sons, Inc.
TL;DR: From a decisional point of view, it would be better to consider firm A as preferred to firm B, and not simply “discernible”, with respect to the attribute in question, within the original rough set approach.
Abstract: As pointed out by Greco, Matarazzo and Slowinski [1] the original rough set approach does not consider criteria, i.e. attributes with ordered domains. However, in many real problems the ordering properties of the considered attributes may play an important role. E.g. in a bankruptcy evaluation problem, if firm A has a low value of the debt ratio (Total debt/Total assets) and firm B has a large value of the same ratio, within the original rough set approach the two firms are just discernible, but no preference is established between them two with respect to the attribute “debt ratio”. Instead, from a decisional point of view, it would be better to consider firm A as preferred to firm B, and not simply “discernible”, with respect to the attribute in question.
TL;DR: A counterexample is constructed theoretically, which demonstrates that these strategies for the minimal attribute reduction with polynomial time complexity are all incomplete with respect to the minimal reduction.
Abstract: Several strategies for the minimal attribute reduction with polynomial time complexity (O(n
k
)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM), a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.
TL;DR: The theory of imprecision of spatial data resulting from finite granularities is extended to a model that includes both spatial and semantic components, and notions such as observation, schema, frame of discernment and vagueness are examined and formalised.
TL;DR: This work considers the problem of searching for a minimal set of cuts on attribute domains that preserves discernibility of objects with respect to any chosen attributes subset of cardinality s (where s is a parameter given by a user).
Abstract: We study the relationship between reduct problem in Rough Sets theory and the problem of real value attribute discretization. We consider the problem of searching for a minimal set of cuts on attribute domains that preserves discernibility of objects with respect to any chosen attributes subset of cardinality s (where s is a parameter given by a user). Such a discretization procedure assures that one can keep all reducts consisting of at least s attributes. We show that this optimization problem is NP-hard and it is interesting to find efficient heuristics for solving this problem.
01 Jan 1998
TL;DR: This paper investigates Rough Set Systems within the framework of Nelson algebras and the structure of the resulting subclass is inherently described using the properties of Approximation Spaces, achieving in a quite “natural” way an interpretation based on the notion of Chain Based Lattice.
Abstract: Any Rough Set System induced by an Approximation Space can be given several logic-algebraic interpretations related to the intuitive reading of the notion of Rough Set. In this paper Rough Set Systems are investigated, first, within the framework of Nelson algebras and the structure of the resulting subclass is inherently described using the properties of Approximation Spaces. In particular, the logic-algebraic structure given to a Rough Set System, understood as a Nelson algebra is equipped with a weak negation and a strong negation and, since it is a finite distributive lattice, it can also be regarded as a Heyting algebra equipped with its own pseudo-complementation. The double weak negation and the double pseudo-complementation are shown to be projection operations connected to the notion of definability in Approximation Spaces. From this analysis we obtain an interpretation of Rough Sets Systems connected to three-valued Lukasiewicz algebras where the roles of projections operators are played by the two endomorphisms of these algebras. Finally, continuing to explore the point of view of Multi-Valued Logics suggested by the latter interpretation we achieve in a quite “natural” way an interpretation based on the notion of Chain Based Lattice. Here the projection operators are provided by the pseudo-supplementation and dual pseudo-supplementation.