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
Buszkowski W. and Orlowska E. (1986): On the Logic of Database Dependencies, Bull. Polish Acad. Sci. Math. vol. 34, 345–354
Casti J. L. (1989): Alternate Realities - Mathematical Models of Nature and Man, John Wiley and Sons
Codd, E.F. (1970): A Relational Model of Data for Large Shared Data Banks, Comm. ACM. vol. 13, 377–387
Chen K.H., Ras Z. and Skowron A. (1988): Attributes and Rough Properties in Information Systems, Internat.J.Approx.Reason. 2 (4), 365–376
Garey M.R. and Johnson D.S., (1979): Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman and Company, San Francisco
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
Glazek K. (1979): Some Old and New Problems in the Independence Theory, Colloquium Mathematicum vol. 17, 127–189
Halpern J.Y. ed. (1986): Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann
Hurley R. B. (1983): Decision Tables in Software Engineering, Van Nostrand Reinhold Company, New York
Kautz W.H. (1968): Fault Testing and Diagnosis in Combinational Digital Circuits, IEEE Transactions on Computers, April, 352–366
Lipski W. Jr. (1979): On Semantic Issues Connected with Incomplete Information Databases, ACM Transactions on Database Systems vol. 4, 269–296
Lipski W. Jr. (1981): On Databases with Incomplete Information, Journal of the ACM. vol. 28, 41–70
Los J. (1979): Characteristic Sets of a System of Equivalence Relations, Colloquium Mathematicum XLII, 291–293
Marczewski E. (1958): A general Scheme of Independence in Mathematics, BAPS, 731–736
Moshkov M.Iu., (1982): On the Conditional Tests (in Russian), Dokl. Akad. Nauk SSSR 265 (2), 550–552.
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
Novotny M. and Pawlak Z. (1988): Independence of Attributes, Bull. Polish Acad. Sci. Math. vol. 36, 459–465
Novotny M. and Pawlak Z. (1988): Partial Dependency of Attributes Bull. Polish Acad. Sci. Math.vol. 36, 453–458
Novotny M. and Pawlak Z. (1989): Algebraic Theory of Independence in Information Systems, Institute of Mathematics Czechoslovak Academy of Sciences Report 51
Orlowska E. (1983): Dependencies of Attributes in Pawlak’s Information Systems, Fundamenta Informaticae vol. 6, 247–256
Orlowska E. and Pawlak Z. (1984): Expressive Power of Knowledge Representation Systems, International Journal of Man-Machine Studies vol. 20, 485–500
Orlowska E. and Pawlak Z. (1984): Representation of Nondeterministic Information, Theoretical Computer Science vol. 29, 27–39
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
Pawlak Z. (1981): Information Systems - Theoretical Foundations, ( The book in Polish ), PWN Warsaw
Pawlak Z. (1981): Information Systems–Theoretical Foundations, Information Systems vol. 6, 205–218
Pawlak Z. (1982): Rough sets, International Journal of Information and Computer Science vol. 11, 344–356
Pawlak Z. (1985): On Rough Dependency of Attributes in Information Systems, Bull. Polish Acad. Sci. Tech. vol. 33, 481–485
Pawlak Z. and Rauszer C. M. (1985): Dependency of Attributes in Information Systems, Bull. Polish Acad. Sci. Math. vol. 33, 551–559
Pawlak Z. (1991): Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer
Parikh R. ed. (1990): Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann
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
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
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
Rauszer C. M. (1985): An Algebraic and Logical Approach to Indiscernibility Relations, ICS PAS Reports No 559
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
Rauszer C. M. (1988): Algebraic Properties of Functional Dependencies, Bull. Polish Acad. Sci. Math. vol. 33, 561–569
Rauszer C.: Decision Logic, to appear in Fundamenta Informaticae
Salton G. (1968): Automatic Information Organization and Retrieval, McGraw-Hill, New York
Skowron A. (1988): On Topology in Information Systems, Bull. Acad. Polon. Sci. Math. vol. 36, pp. 477–479
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
Skowron A. and Stepaniuk J. (1991): Towards an Approximation Theory of Discrete Problems: Part I, Fundamenta Informaticae 15 (2), 187–208
Skowron A. (1991): The Discernibility Matrix and Function in Information System, manuscript
Truszczynski M., (1982): Algorithmic Aspects of the Minimization of the Set of Attribute Problems, Fundamenta Informaticae 4 (4)
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
Vakarelov D. (1989): Modal Logics for Knowledge Representation Systems,LNCS vol.363: 257–277
Wegener I. (1987): The Complexity of Boolean Functions, John Wiley and Sons
Wille R. (1982): Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts, In: I.Rival (Ed.), Ordered Sets, Reidel, Dordrecht-Boston, 445–470
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
Ziarko W. (1988): Acquisition of Design Knowledge from Examples, Math. Comput. Modeling vol. 10, 551–554
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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
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