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The Discernibility Matrices and Functions in Information Systems

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Book cover Intelligent Decision Support

Part of the book series: Theory and Decision Library ((TDLD,volume 11))

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.

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References

  1. Buszkowski W. and Orlowska E. (1986): On the Logic of Database Dependencies, Bull. Polish Acad. Sci. Math. vol. 34, 345–354

    MathSciNet  MATH  Google Scholar 

  2. Casti J. L. (1989): Alternate Realities - Mathematical Models of Nature and Man, John Wiley and Sons

    Google Scholar 

  3. Codd, E.F. (1970): A Relational Model of Data for Large Shared Data Banks, Comm. ACM. vol. 13, 377–387

    Article  MATH  Google Scholar 

  4. Chen K.H., Ras Z. and Skowron A. (1988): Attributes and Rough Properties in Information Systems, Internat.J.Approx.Reason. 2 (4), 365–376

    Article  MathSciNet  MATH  Google Scholar 

  5. Garey M.R. and Johnson D.S., (1979): Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman and Company, San Francisco

    MATH  Google Scholar 

  6. Grzymala-Busse J., (1986): On the Reduction of Knowledge Representation Systems, Proc. of the 6-th International Workshop on Expert Systems and their Applications, Avignon, France, April 28–30, 463–478

    Google Scholar 

  7. Glazek K. (1979): Some Old and New Problems in the Independence Theory, Colloquium Mathematicum vol. 17, 127–189

    MathSciNet  Google Scholar 

  8. Halpern J.Y. ed. (1986): Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann

    Google Scholar 

  9. Hurley R. B. (1983): Decision Tables in Software Engineering, Van Nostrand Reinhold Company, New York

    Google Scholar 

  10. Kautz W.H. (1968): Fault Testing and Diagnosis in Combinational Digital Circuits, IEEE Transactions on Computers, April, 352–366

    Google Scholar 

  11. Lipski W. Jr. (1979): On Semantic Issues Connected with Incomplete Information Databases, ACM Transactions on Database Systems vol. 4, 269–296

    Article  Google Scholar 

  12. Lipski W. Jr. (1981): On Databases with Incomplete Information, Journal of the ACM. vol. 28, 41–70

    Article  MathSciNet  MATH  Google Scholar 

  13. Los J. (1979): Characteristic Sets of a System of Equivalence Relations, Colloquium Mathematicum XLII, 291–293

    Google Scholar 

  14. Marczewski E. (1958): A general Scheme of Independence in Mathematics, BAPS, 731–736

    Google Scholar 

  15. Moshkov M.Iu., (1982): On the Conditional Tests (in Russian), Dokl. Akad. Nauk SSSR 265 (2), 550–552.

    Google Scholar 

  16. Mrozek A. (1987): Rough Sets and Some Aspects of Expert Systems Realization, Proc. 7-th Internat. Workshop on Expert Systems and their Applications, Avignon, France, 597–611

    Google Scholar 

  17. Novotny M. and Pawlak Z. (1988): Independence of Attributes, Bull. Polish Acad. Sci. Math. vol. 36, 459–465

    MathSciNet  MATH  Google Scholar 

  18. Novotny M. and Pawlak Z. (1988): Partial Dependency of Attributes Bull. Polish Acad. Sci. Math.vol. 36, 453–458

    MathSciNet  MATH  Google Scholar 

  19. Novotny M. and Pawlak Z. (1989): Algebraic Theory of Independence in Information Systems, Institute of Mathematics Czechoslovak Academy of Sciences Report 51

    Google Scholar 

  20. Orlowska E. (1983): Dependencies of Attributes in Pawlak’s Information Systems, Fundamenta Informaticae vol. 6, 247–256

    MathSciNet  MATH  Google Scholar 

  21. Orlowska E. and Pawlak Z. (1984): Expressive Power of Knowledge Representation Systems, International Journal of Man-Machine Studies vol. 20, 485–500

    Article  MATH  Google Scholar 

  22. Orlowska E. and Pawlak Z. (1984): Representation of Nondeterministic Information, Theoretical Computer Science vol. 29, 27–39

    Article  MathSciNet  Google Scholar 

  23. Pagliani P. (1987): Polystructured Model Spaces as Algorithm Oriented Models for Approximation Spaces and Pawlak’s Information Systems, Facolta di Science dell Informazione, Internal Raport PAG /3

    Google Scholar 

  24. Pawlak Z. (1981): Information Systems - Theoretical Foundations, ( The book in Polish ), PWN Warsaw

    Google Scholar 

  25. Pawlak Z. (1981): Information Systems–Theoretical Foundations, Information Systems vol. 6, 205–218

    Article  MATH  Google Scholar 

  26. Pawlak Z. (1982): Rough sets, International Journal of Information and Computer Science vol. 11, 344–356

    MathSciNet  Google Scholar 

  27. Pawlak Z. (1985): On Rough Dependency of Attributes in Information Systems, Bull. Polish Acad. Sci. Tech. vol. 33, 481–485

    MathSciNet  MATH  Google Scholar 

  28. Pawlak Z. and Rauszer C. M. (1985): Dependency of Attributes in Information Systems, Bull. Polish Acad. Sci. Math. vol. 33, 551–559

    MathSciNet  MATH  Google Scholar 

  29. Pawlak Z. (1991): Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer

    Book  MATH  Google Scholar 

  30. Parikh R. ed. (1990): Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann

    Google Scholar 

  31. Rasiowa H. and Skowron A., (1986): Approximation Logic, In: Mathematical Methods of Specification and Synthesis of Software Systems ‘85, Akademie-Verlag Berlin, Band 31, 123–139

    Chapter  Google Scholar 

  32. Rauszer C. M. (1984): An Equivalence Between Indiscernibility Relations in Information Systems and a Fragment of Intuitionistic Logic, Lecture Notes in Computer Science vol. 208, Springer Verlag, 298–317

    Google Scholar 

  33. Rauszer C. M. (1985): An Equivalence between Theory of Functional Dependencies and Fragment of Intuitionistic Logic, Bull. Polish Acad. Sci. Math. vol. 33, 571–679

    MathSciNet  MATH  Google Scholar 

  34. Rauszer C. M. (1985): An Algebraic and Logical Approach to Indiscernibility Relations, ICS PAS Reports No 559

    Google Scholar 

  35. Rauszer C. M. (1987): Algebraic and Logical Description of Functional and Multivalued Dependencies. Proc of the Sec. Int. Symp. on Methodologies for Intelligent Systems. October 17, Charlotte, North Holland 1987, 145–155

    Google Scholar 

  36. Rauszer C. M. (1988): Algebraic Properties of Functional Dependencies, Bull. Polish Acad. Sci. Math. vol. 33, 561–569

    MathSciNet  Google Scholar 

  37. Rauszer C.: Decision Logic, to appear in Fundamenta Informaticae

    Google Scholar 

  38. Salton G. (1968): Automatic Information Organization and Retrieval, McGraw-Hill, New York

    Google Scholar 

  39. Skowron A. (1988): On Topology in Information Systems, Bull. Acad. Polon. Sci. Math. vol. 36, pp. 477–479

    MathSciNet  MATH  Google Scholar 

  40. Skowron A. (1990): An Approach to Synthesis of Decision Algorithms in Interaction with Knowledge Bases and Environment. An Example Based on Some Glaucoma Processes (in cooperation with Medical Center in Warsaw), manuscript pp.1–173, Warsaw

    Google Scholar 

  41. Skowron A. and Stepaniuk J. (1991): Towards an Approximation Theory of Discrete Problems: Part I, Fundamenta Informaticae 15 (2), 187–208

    MathSciNet  MATH  Google Scholar 

  42. Skowron A. (1991): The Discernibility Matrix and Function in Information System, manuscript

    Google Scholar 

  43. Truszczynski M., (1982): Algorithmic Aspects of the Minimization of the Set of Attribute Problems, Fundamenta Informaticae 4 (4)

    Google Scholar 

  44. Vakarelov D. (1987): Abstract Characterization of Some Modal Knowledge Representation Systems and the Logic NIL of Nondeterministic Information, In: Jorraud, Ph. and Squrev, V. (ed.) Artificial Intelligence I I, Methodology, Systems, Applications, North Holland

    Google Scholar 

  45. Vakarelov D. (1989): Modal Logics for Knowledge Representation Systems,LNCS vol.363: 257–277

    MathSciNet  Google Scholar 

  46. Wegener I. (1987): The Complexity of Boolean Functions, John Wiley and Sons

    Google Scholar 

  47. Wille R. (1982): Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts, In: I.Rival (Ed.), Ordered Sets, Reidel, Dordrecht-Boston, 445–470

    Chapter  Google Scholar 

  48. Ziarko W. (1987): On Reduction of Knowledge Representation, Proc. 2-nd International Symp.on Methodologies of for Intelligent Systems, Charlotte USA, North Holland, 99–113

    Google Scholar 

  49. Ziarko W. (1988): Acquisition of Design Knowledge from Examples, Math. Comput. Modeling vol. 10, 551–554

    Article  Google Scholar 

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© 1992 Springer Science+Business Media Dordrecht

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Skowron, A., Rauszer, C. (1992). The Discernibility Matrices and Functions in Information Systems. In: Słowiński, R. (eds) Intelligent Decision Support. Theory and Decision Library, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7975-9_21

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  • DOI: https://doi.org/10.1007/978-94-015-7975-9_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4194-4

  • Online ISBN: 978-94-015-7975-9

  • eBook Packages: Springer Book Archive

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