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Journal ArticleDOI

Data analysis based on discernibility and indiscernibility

15 Nov 2007-Information Sciences (Elsevier)-Vol. 177, Iss: 22, pp 4959-4976
TL;DR: The consideration of the matrix- counterpart of relations, and the relation-counterpart of matrices, brings more insights into rough set theory.
About: This article is published in Information Sciences.The article was published on 2007-11-15. It has received 128 citations till now.
Citations
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Journal ArticleDOI
TL;DR: The structures of the lower and upper approximations based on arbitrary binary relations in the generalized rough sets are presented and an algorithm to compute atoms for these two Boolean algebras is presented.

229 citations

Journal ArticleDOI
TL;DR: This paper introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure, and presents a generalization of the classical rough set framework for data-based attribute selection and reduction using fuzzy tolerance relations.

227 citations


Cites methods from "Data analysis based on discernibili..."

  • ...Therefore, within the context of fuzzy rough set theory, we present a generalization of the classical rough set framework for databased attribute selection and reduction using fuzzy tolerance relations....

    [...]

Journal ArticleDOI
TL;DR: A formal approach to granular computing with multi-scale data measured at different levels of granulations is proposed in this paper and the unravelling of decision rules at different scales in multi- scale decision tables is discussed.

202 citations

Journal ArticleDOI
TL;DR: This study suggests that hybrid credit scoring approach is mostly robust and effective in finding optimal subsets and is a promising method to the fields of data mining.
Abstract: The credit scoring has been regarded as a critical topic and its related departments make efforts to collect huge amount of data to avoid wrong decision. An effective classificatory model will objectively help managers instead of intuitive experience. This study proposes four approaches combining with the SVM (support vector machine) classifier for features selection that retains sufficient information for classification purpose. Different credit scoring models are constructed by selecting attributes with four approaches. Two UCI (University of California, Irvine) data sets are chosen to evaluate the accuracy of various hybrid-SVM models. SVM classifier combines with conventional statistical LDA, Decision tree, Rough sets and F-score approaches as features pre-processing step to optimize feature space by removing both irrelevant and redundant features. In this paper, the procedure of the proposed approaches will be described and then evaluated by their performances. The results are compared in combination with SVM classifier and nonparametric Wilcoxon signed rank test will be held to show if there is any significant difference between these models. The result in this study suggests that hybrid credit scoring approach is mostly robust and effective in finding optimal subsets and is a promising method to the fields of data mining.

192 citations

Journal ArticleDOI
TL;DR: This paper deals with attribute reduction in incomplete information systems and incomplete decision systems based on Dempster-Shafer theory of evidence and shows that in an incomplete information system an attribute set is a belief reduct if and only if it is a classical reduct and a plausibility consistent set must be a classical consistent set.

183 citations

References
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Book
31 Oct 1991
TL;DR: Theoretical Foundations.
Abstract: I. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician's Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.

7,826 citations

Book ChapterDOI
01 Jan 1992
TL;DR: In this article, the authors introduce two notions related to any information system, namely the discernibility matrix and discernibility function, and obtain several algorithms for solving problems related among other things to the rough definability, reducts, core and dependencies generation.
Abstract: We introduce two notions related to any information system, namely the discernibility matrix and discernibility function. We present some properties of these notions and as corollaries we obtain several algorithms for solving problems related among other things to the rough definability, reducts, core and dependencies generation.

1,529 citations

Journal ArticleDOI
Yiyu Yao1
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


"Data analysis based on discernibili..." refers background in this paper

  • ...The research on quantitative indiscernibility relations has led to the study based on blocks [4,5], templates [1,9], rough inclusion [16,20], and tolerance, similarity or neighborhood relations [11,33,34]...

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  • ...Examples of such studies include valued-similarity and tolerance [17,25,26,35], neighborhood systems [11,33,34], rough inclusion [16,20], and many more....

    [...]

Journal ArticleDOI
TL;DR: New definitions of lower and upper approximations are proposed, which are basic concepts of the rough set theory and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.
Abstract: This paper proposes new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from the concept of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.

963 citations

Book
01 Aug 1992
TL;DR: The use of 'Rough Sets' Methods to draw Premonitory Factors for Earthquakes by emphasising Gas Geochemistry: The Case of a Low Seismic Activity Context in Belgium J.T. Polkowski is used.
Abstract: Preface Z. Pawlak. Scope and Goals of the Book R. Slowinski. Part I: Applications of the Rough Sets Approach to Intelligent Decision Support. 1. LERS -- A System for Learning from Examples Based on Rough Sets J.W. Grzymala-Busse. 2. Rough Sets in Computer Implemetation of Rule-Based Control of Industrial Process A. Mrozek. 3. Analysis of Diagnostic Symptoms in Vibroacoustic Diagnostic by Means of the Rough Sets Theory R. Nowicki, R. Slowinski, J. Stefanowski. 4. Knowledge-Based Process Control Using Rough Sets A.J. Szladown, W.P. Ziarko. 5. Acquisition of Control Algorithms from Operation Data W.P. Ziarko. 6. Rough Classification of HSV Patients K. Slowinski. 7. Surgical Wound Infection -- Conducive Factors and their Mutual Dependencies M. Kandulski, J. Marciniec, K. Tukallo. 8. Fuzzy Inference System Based on Rough Sets and its Application to Medical Diagnosis H. Tanaka, H. Ishibuchi, T. Shigenaga. 9. Analysis of Structure-Activity Relationships of Quaternary Ammonium Compounds J. Krysinski. 10. Rough Sets-Based Study of Voter Preference in 1988 U.S.A. Presidential Election M. Hadjimichale, A. Wasilewska. 11. An Application of Rough Set Theory in the Control of Water Conditions in a Polder A. Reinhard, B. Stawski, T. Weber, U. Wybraniec-Skardowska. 12. Use of 'Rough Sets' Methods to draw Premonitory Factors for Earthquakes by emphasising Gas Geochemistry: The Case of a Low Seismic Activity Context in Belgium J. Teghem, J.-M. Charlet. 13. Rough Sets and Some Aspects of Logic Synthesis T. Luba,J. Rybnik. Part II: Comparison with Related Methodologies. 1. Putting Rough Sets and Fuzzy Sets together D. Dubois, H. Prade. 2. Applications of Fuzzy-Rough Classification to Logics A. Nakamura. 3. Comparison of the Rough Sets Approach and Probalistic Data Analysis Techniques on a Common Set of Medical Data E. Krusinska, A. Babic, R. Slowinski, J. Stefanowski. 4. Some Experiments to Compare Rough Sets Theory and Ordinal Statistical Methods J. Teghem, M. Benjelloun. 5. Topological and Fuzzy Rough Sets T. Lin. 6. On Convergence of Rough Sets L.T. Polkowski. Part III: Further Developments. 1. Maintenance of Knowledge in Dynamic Systems M.E. Orlowska, M.W. Orlowski. 2. The Discernibility Matrices and Functions in Information Systems A. Skowron, C. Rauszer. 3. Sensitivity of Rough Classification to Changes in Norms of Attributes K. Slowinski, R. Slowinksi. 4. Discretization of Condition Attributes Space A. Lenarcik, Z. Piasta. 5. Consequence Relations and Information Systems D. Vakarelov. 6. Rough Grammar for High Performance Management of Processes on a Distributed System Z.M. Wojcik, B.E. Wojcik. 7. Learning Classification Rules from Database in the Context of Knowledge-Acquisition and Representation R. Yasdi. 8. 'RoughDAS' and 'RoughClass' Software Implementations of the Rough Sets Approach R. Slowinski, J. Stefanowski. Appendix: Glossary of Basic Concepts. Subject Index.

875 citations