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Dependence Spaces of Information Systems

  • Miroslav Novotný
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 13)

Abstract

A general model is introduced and investigated of a great variety of finite structures studied in computer science. The model is referred to as dependence space. The main feature of the model is that it enables us to deal with the indiscernibility-type incompleteness of information that a modelled structure might be burdened with. The model provides a general framework for expressing the concept of independence of a set and the concept of dependency between sets with respect to a dependence space. It is shown that these concepts lay the foundation on which many applied structures rest. The theory of dependence spaces is developed aimed at providing tools for studying the problems relevant for the modelled structures.

Keywords

Boolean Algebra Nonempty Subset Closure Operator Dependence Relation Great Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Bil]
    Birkhoff, G.: Lattice Theory. Third edition, American Math. Society, Provi-dence, (1984)Google Scholar
  2. [BB1]
    Birkhoff, G., Bartee, T.C.: Modern Applied Algebra. McGraw Hill, New York, (1970)MATHGoogle Scholar
  3. [Bol]
    Boruvka, O.: Grundlagen der Gruppoid-und Gruppentheorie. VEB Deutscher Verlag der Wissenschaften, Berlin, (1960)MATHGoogle Scholar
  4. [Cel]
    Cendrowska, J.: PRISM: An algorithm for inducing modular rules. Int. J. Man-Machine Studies, 27, (1987), 349 - 370MATHCrossRefGoogle Scholar
  5. [Dul]
    Duda, J.: Boolean concept lattices and good contexts. Cas. Pést. Mat. 114, (1989), 165 - 175MathSciNetMATHGoogle Scholar
  6. [GJ1]
    Garey, M.R., Johnson, D.S.: Computers and intractability. A guide to the theory of NP-completeness. W.H. Freeman and Co., San Francisco, (1979)Google Scholar
  7. [Gel]
    Gentzen, G.: Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39, (1935), 176 - 210MathSciNetCrossRefGoogle Scholar
  8. [G11]
    Glazek, K.: Some old and new problems of the independence in mathematics. Colloquium Math., 17, (1979), 127 - 189MathSciNetGoogle Scholar
  9. [HNP1]
    Haupt, O., Nöbeling, G., Pauc, C.: fiber Abhängigkeitsräume. J. Reine Angew. Math., 181, (1940), 193 - 217Google Scholar
  10. [Lil]
    Lipski, W., Jr.: Two NP-complete problems related to information retrieval. Fundamentals of Computation Theory. Lecture Notes in Computer Science, 56, Springer, Berlin, (1977), 452 - 458Google Scholar
  11. [LO1]
    Lucchesi, C.L., Osborn, S.L.: Candidate keys for relations. J. Comput. System Sci., 17, (1978), 270 - 279MathSciNetMATHCrossRefGoogle Scholar
  12. [Mal]
    Marczewski, E.: A general scheme of independence in mathematics. Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys., 6, (1958), 731 - 736MathSciNetMATHGoogle Scholar
  13. [MP1]
    Marek, W., Pawlak, Z.: Mathematical foundations of information storage and retrieval I, II, III. CC PAS Reports, 135, 136, 137, Warszawa, (1973)Google Scholar
  14. MP2] Marek, W., Pawlak, Z.: Information storage and retrieval system - mathematical foundations. CC PAS Reports, 149,Warszawa, (1974). Also in: Theoretical Computer Science, 1,(1976), 331-354Google Scholar
  15. [Mil]
    Mrózek, A.: Rough sets and some aspects of expert system realization. 7th International Workshop on Expert Systems and their Applications, Avignon, (1987), 597 - 611Google Scholar
  16. [Mr2]
    Mrózek, A.: Rough sets and dependency analysis among attributes in computer implementation of expert’s inference models. Int. J. Man-Machine Studies, 30, (1989), 457 - 473MATHCrossRefGoogle Scholar
  17. NoJ1] Novotnÿ, J.: Application of information systems to evaluation of pedagogical research. (Czech). To appear in Sbornik praci pedagogické fakulty Masarykovy Univerzity (Publications of the Pedagogical Faculty, Masaryk University, Brno, (1993))Google Scholar
  18. [NN1]
    Novotnÿ, J., Novotnÿ, M.: Notes on the algebraic approach to dependence in information systems. Fundamenta Informaticae, 16, (1992), 263 - 273MathSciNetMATHGoogle Scholar
  19. [NN2]
    Novotnÿ, J., Novotnÿ, M.: On dependence in Wille’s contexts. Fundamenta Informaticae, 19, (1993), 343 - 353MathSciNetMATHGoogle Scholar
  20. [NoMi]
    Novotnÿ, M.: On sequents defined by means of information systems. Fundamenta Informaticae, 4, (1981), 1041 - 1048MathSciNetMATHGoogle Scholar
  21. [NoM2]
    Novotnÿ, M.: Remarks on sequents defined by means of information systems. Fundamenta Informaticae, 6, (1983), 71 - 79MathSciNetMATHGoogle Scholar
  22. [NP1]
    Novotnÿ, M., Pawlak, Z.: On a representation of rough sets by means of information systems. Fundamenta Informaticae, 6, (1983), 289 - 296MathSciNetMATHGoogle Scholar
  23. [NP2]
    Novotnÿ, M., Pawlak, Z.: Characterization of rough top equalities and rough bottom equalities. Bull. Polish Acad. Sci. Math., 33, (1985), 91 - 97MathSciNetMATHGoogle Scholar
  24. [NP3]
    Novotnÿ, M., Pawlak, Z.: On rough equalities. Bull. Polish Acad. Sci. Math., 33, (1985), 99 - 104MathSciNetMATHGoogle Scholar
  25. [NP4]
    Novotnÿ, M., Pawlak, Z.: Black box analysis and rough top equality. Bull. Acad. Sci. Math., 33, (1985), 105 - 113MATHGoogle Scholar
  26. [NP5]
    Novotnÿ, M., Pawlak, Z.: Concept forming and black boxes. Bull. Polish Acad. Sci. Math., 35, (1987), 133 - 141MathSciNetMATHGoogle Scholar
  27. [NP6]
    Novotnÿ, M., Pawlak, Z.: Partial dependency of attributes. Bull. Polish Acad. Sci. Math., 36, (1988), 453 - 458MathSciNetMATHGoogle Scholar
  28. [NP7]
    Novotnÿ, M., Pawlak, Z.: Independence of attributes. Bull. Polish Acad. Sci. Math., 36, (1988), 459 - 465MathSciNetMATHGoogle Scholar
  29. [NP8]
    Novotnÿ, M., Pawlak, Z.: On superreducts. Bull. Polish Acad. Sci. Tech. Sci., 38, (1990), 101 - 112MATHGoogle Scholar
  30. [NP9]
    Novotnÿ, M., Pawlak, Z.: Algebraic theory of independence in information systems. Fundamenta Informaticae, 14, (1991), 454 - 476MathSciNetMATHGoogle Scholar
  31. [NP10]
    Novotnÿ, M., Pawlak, Z.: On a problem concerning dependence spaces. Fundamenta Informaticae, 16, (1992), 275 - 287MathSciNetMATHGoogle Scholar
  32. Pal] Pawlak, Z.: Mathematical foundations of information retrieval. CC PAS Reports, 101,(1973), WarszawaGoogle Scholar
  33. [Pa2]
    Pawlak, Z.: Information systems. ICS PAS Reports, 338, Warszawa, (1978)Google Scholar
  34. [Pa3]
    Pawlak, Z.: Rough sets. ICS PAS Reports, 431, Warszawa, (1981)Google Scholar
  35. [Pa4]
    Pawlak, Z.: Rough sets. Algebraic and topological approach. Intern. Journ. of Computer and Information Sciences, 11, (1982), 341 - 366MathSciNetMATHCrossRefGoogle Scholar
  36. [Pa5]
    Pawlak, Z.: Systemy informacyjne, podstawy teoretyczne (Information systems, theoretical foundations). Wydawnictwa Naukowo-Techniczne, Warszawa, (1983)Google Scholar
  37. [Pa6]
    Pawlak, Z.: Learning from examples — the case of an imperfect teacher. Bull. Polish Acad. Sci. Tech., 35, (1987), 259 - 264MathSciNetMATHGoogle Scholar
  38. [Pa7]
    Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht — Boston — London, (1991)MATHGoogle Scholar
  39. [Rai]
    Rauszer, C.M.: Reducts in information systems. Fundamenta Informaticae, 15, (1991), 1 - 12MathSciNetMATHGoogle Scholar
  40. [Szl]
    Sz sz, G.: Introduction to Lattice Theory. Academic Press, Budapest, (1963)Google Scholar
  41. [Wil]
    Wille, R.: Restructuring lattice theory. In: Ordered Sets (Ed. I. Rival ), Reidel, Dordrecht — Boston, (1982), 445 - 470CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Miroslav Novotný
    • 1
  1. 1.Masaryk UniversityBrnoCzech Republic

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