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Arrow Decision Logic for Relational Information Systems

  • Conference paper
Book cover Transactions on Rough Sets V

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 4100))

Abstract

In this paper, we propose an arrow decision logic (ADL) for relational information systems (RIS). The logic combines the main features of decision logic (DL) and arrow logic (AL). DL represents and reasons about knowledge extracted from decision tables based on rough set theory, whereas AL is the basic modal logic of arrows. The semantic models of DL are functional information systems (FIS). ADL formulas, on the other hand, are interpreted in RIS. RIS , which not only specifies the properties of objects, but also the relationships between objects. We present a complete axiomatization of ADL and discuss its application to knowledge representation in multicriteria decision analysis.

A preliminary version of the paper was published in [1].

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References

  1. Fan, T.-F., Liu, D.-R., Tzeng, G.-H.: Arrow decision logic. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 651–659. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Agrawal, R., Srikant, R.: Fast algorithm for mining association rules. In: Proceedings of the 20th International Conference on Very Large Data Bases, pp. 487–499. Morgan Kaufmann Publishers, San Francisco (1994)

    Google Scholar 

  3. Asperti, A., Longo, G.: Categories, Types, and Structures: An Introduction to Category Theory for the Working Computer Scientist. MIT Press, Cambridge (1991)

    MATH  Google Scholar 

  4. Birkhoff, G., Lipson, J.: Heterogeneous algebras. Journal of Combinatorial Theory 8 (1970)

    Google Scholar 

  5. Burris, S.N., Sankappanavar, H.P.: A Course in Universal Algebra. Springer, Heidelberg (1981)

    MATH  Google Scholar 

  6. Cohn, P.M.: Universal Algebra. D. Reidel Publishing Co. (1981)

    Google Scholar 

  7. Fan, T.F., Hu, W.C., Liau, C.J.: Decision logics for knowledge representation in data mining. In: Proceedings of the 25th Annual International Computer Software and Applications Conference, pp. 626–631. IEEE Press, Los Alamitos (2001)

    Google Scholar 

  8. Fan, T.F., Liu, D.R., Tzeng, G.H.: Rough set-based logics for multicriteria decision analysis. In: Proceedings of the 34th International Conference on Computers and Industrial Engineering (2004)

    Google Scholar 

  9. Gabbay, D.M.: An irreflexivity lemma with applications to axiomatization of conditions on linear frames. In: Mönnich, U. (ed.) Aspects of Philosophical Logic, pp. 67–89. D. Reidel Publishing Co. (1981)

    Google Scholar 

  10. Greco, S., Matarazzo, B., Slowinski, R.: Rough set approach to multi-attribute choice and ranking problems. In: Proceedings of the 12th International Conference on Multiple Criteria Decision Making, pp. 318–329 (1997)

    Google Scholar 

  11. Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation in a pairwise comparison table. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Data Mining and Knowledge Discovery, pp. 13–36. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  12. Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation by dominance relations. European Journal of Operational Research 117(1), 63–83 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Greco, S., Matarazzo, B., Slowinski, R.: Extension of the rough set approach to multicriteria decision support. INFOR Journal: Information Systems and Operational Research 38(3), 161–195 (2000)

    Google Scholar 

  14. Greco, S., Matarazzo, B., Slowinski, R.: Rough set theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Greco, S., Matarazzo, B., Slowinski, R.: Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European Journal of Operational Research 138(2), 247–259 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Greco, S., Matarazzo, B., Slowinski, R.: Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158(2), 271–292 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Grzymala-Busse, J.W.: Algebraic properties of knowledge representation systems. In: Proceedings of the ACM SIGART International Symposium on Methodologies for Intelligent Systems, pp. 432–440. ACM Press, New York (1986)

    Chapter  Google Scholar 

  18. Han, J., Kamber, M.: Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, San Francisco (2001)

    Google Scholar 

  19. Liau, C.-J.: Belief reasoning, revision and fusion by matrix algebra. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 133–142. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Liau, C.J.: Matrix representation of belief states: An algebraic semantics for belief logics. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 12(5), 613–633 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Liau, C.J., Lin, T.Y.: Reasoning about relational granulation in modal logics. In: Proc. of the First IEEE International Conference on Granular Computing, pp. 534–538. IEEE Press, Los Alamitos (2005)

    Google Scholar 

  22. Liau, C.-J., Liu, D.-R.: A logical approach to fuzzy data analysis. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 412–417. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  23. Liau, C.J., Liu, D.R.: A possibilistic decision logic with applications. Fundamenta Informaticae 46(3), 199–217 (2001)

    MATH  MathSciNet  Google Scholar 

  24. Marx, M., Venema, Y.: Multi-Dimensional Modal Logic. Kluwer Academic Publishers, Dordrecht (1997)

    MATH  Google Scholar 

  25. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(15), 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  26. Pawlak, Z.: Rough Sets–Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  27. Scott, J.: Social Network Analysis: A Handbook, 2nd edn. Sage Publications, Thousand Oaks (2000)

    Google Scholar 

  28. Skowron, A.: Extracting laws from decision tables. Computational Intelligence: An International Journal 11, 371–388 (1995)

    MathSciNet  Google Scholar 

  29. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support Systems: Handbook of Applications and Advances in Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  30. Skowron, A., Świniarski, R.W.: Rough sets and higher order vagueness. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 33–42. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  31. Skowron, A., Synak, P.: Complex patterns. Fundamenta Informaticae 60(1-4), 351–366 (2004)

    MATH  MathSciNet  Google Scholar 

  32. Słowiński, R., Greco, S., Matarazzo, B.: Rough set analysis of preference-ordered data. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 44–59. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  33. Venema, Y.: A crash course in arrow logic. In: Marx, M., P’olos, L., Masuch, M. (eds.) Arrow Logic and Multi-Modal Logic, pp. 3–34. CSLI Publications, Stanford (1996)

    Google Scholar 

  34. Yao, Y.Y., Liau, C.J.: A generalized decision logic language for granular computing. In: Proceedings of the 11th IEEE International Conference on Fuzzy Systems, pp. 773–778. IEEE Press, Los Alamitos (2002)

    Google Scholar 

  35. Yao, Y.Y., Liu, Q.: A generalized decision logic in interval-set-valued information tables. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 285–293. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information Management, National Chiao-Tung University, Hsinchu, 300, Taiwan

    Tuan-Fang Fan & Duen-Ren Liu

  2. Department of Computer Science and Information Engineering, National Penghu University, Penghu, 880, Taiwan

    Tuan-Fang Fan

  3. Institute of Management of Technology, National Chiao-Tung University, Hsinchu, 300, Taiwan

    Gwo-Hshiung Tzeng

  4. Department of Business Administration, Kainan University, Taoyuan, 338, Taiwan

    Gwo-Hshiung Tzeng

Authors
  1. Tuan-Fang Fan
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  2. Duen-Ren Liu
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  3. Gwo-Hshiung Tzeng
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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© 2006 Springer-Verlag Berlin Heidelberg

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Fan, TF., Liu, DR., Tzeng, GH. (2006). Arrow Decision Logic for Relational Information Systems. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets V. Lecture Notes in Computer Science, vol 4100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847465_12

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  • DOI: https://doi.org/10.1007/11847465_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39382-5

  • Online ISBN: 978-3-540-39383-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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