Granular Logic with Closeness Relation ‘‘∼λ"``\sim_{\lambda}"‘‘∼λ​" and Its Reasoning (original) (raw)

References

  1. Zadeh, L.A.: Fuzzy Sets and Information Granularity. In: Gupta, M., Ragade, R., Yager, R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland, Amsterdam (1979)
    Google Scholar
  2. Zadeh, L.A.: Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems. In: Soft Computing, vol. 2, pp. 23–25. Springer, Berlin (1998)
    Google Scholar
  3. Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in hunan reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 111–127 (1997)
    Article MATH MathSciNet Google Scholar
  4. Chakraborty, M.K., Banerjee, M.: Rough logic with rough quantifiers. Warsaw University of Technology, ICS Research Report 49/93 (1993)
    Google Scholar
  5. Pawlak, Z.: Rough sets – Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)
    MATH Google Scholar
  6. Liu, Q., Huang, Z.H.: G-Logic and Its Resolution Reasoning. Chinese Journal of Computer (In Chinese) 27(7), 865–873 (2004)
    MathSciNet Google Scholar
  7. Liu, Q.: The OI-resolution of operator rough logic. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, p. 432. Springer, Heidelberg (1998)
    Chapter Google Scholar
  8. Stepaniuk, J.: Rough Relations and Logics. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery I, pp. 248–260. Physica, Heideberg (1998)
    Google Scholar
  9. Liu, Q.: _λ_-Level Rough Equality Relation and the Inference of Rough Paramodulation. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 462–469. Springer, Heidelberg (2001)
    Chapter Google Scholar
  10. Skowron, A.: Toward intelligent systems: Calculi of information granules. In: Proc. of RSTGC 2001, Bulletin of International Rough Set Society, Japan, vol. 5(1/2), pp. 9–30 (2001)
    Google Scholar
  11. Skowron, A., Stepaniuk, J.: Extracting patterns using information granules. In: Proc. of RSTGC 2001, Bulletin of International Rough Set Society, Japan, vol. 5(1/2), pp. 135–142 (2001)
    Google Scholar
  12. Liu, Q., Liu, S.H., Zheng, F.: Rough logic and its applications in data mining. Journal of Software 12(3), 415–419 (2001)
    Google Scholar
  13. Rasiowa, H., Skowron, A.: Rough concepts logic. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 288–297. Springer, Heidelberg (1985)
    Google Scholar
  14. Lin, T.Y., Liu, Q.: First-order rough logic I: Approximate reasoning via rough sets. Fundamenta Informaticae 27(2-3), 137–154 (1996)
    MATH MathSciNet Google Scholar
  15. Wang, X.J.: Introduction for mathematical logic. Press of Beijing Uni., Beijing (1982)
    Google Scholar
  16. Hamilton, A.G.: Logic For Mathematicians. Cambridge Uni. Press, London (1978)
    MATH Google Scholar
  17. Lin, T.Y.: Granular Computing on Binary Relations II: Rough Set Representations and Belief Functions. In: Skowron, A., Polkowski, L. (eds.) Rough Sets In Knowledge Discovery, pp. 121–140. Physica, Berlin (1998)
    Google Scholar
  18. Lin, T.Y.: Granular Computing: Fuzzy Logic and Rough Sets. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words, Information Intelligent Systems, vol. 1, pp. 183–200. Springer, Berlin (1999)
    Google Scholar
  19. Yao, Y.Y., Yao, J.T.: Granular Computing as a Basis for Consistent Classification Problems. In: Proc. of PAKDD 2002 Workshop on Foundations of Data Mining, CIICM, Taiwan, vol. 5, pp. 101–106 (2002)
    Google Scholar
  20. Liu, Q., Liu, Q.: Approximate Reasoning Based on Granular Computing in Granular Logic. In: Proc. of IEEE ICMLS 2002 (2002)
    Google Scholar
  21. Liu, Q.: Granular Language and Its Reasoning, Data Mining and Knowledge Discovery: Theory, Tools, and Technology V. In: Proc. of SPIE 2003, pp. 279–287 (2003)
    Google Scholar
  22. Liu, Q.: Granules and Applications of Granular Computing in Logical Reasoning (In Chinese). Journal of Computer Research and Development 41(4), 546–551 (2004)
    Google Scholar
  23. Liu, Q.: Temporal Rough Logic and Its Application in Data Analysis. Journal of Fudan University (Natural Science) (In Chinese) 43(5), 852–855 (2005)
    Google Scholar
  24. Orlowska, E.: A Logic of Indiscernibility Relation. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 177–186. Springer, Heidelberg (1985)
    Google Scholar
  25. Yao, Y.Y., Liu, Q.: A Generalized Decision Logic in Interval-Set-Valued Information Table. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 285–294. Springer, Heidelberg (1999)
    Chapter Google Scholar
  26. Lin, T.Y.: Granular Computing on Binary Relations-Analysis of Conflict and Chinese Wall Security Policy. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 296–299. Springer, Heidelberg (2002)
    Chapter Google Scholar
  27. Lin, T.Y.: Granular Computing on Binary Relations I: Data Mining and Neighborhood Systems. In: Skowron, A., Polkowski, L. (eds.) Rough Sets In Knowledge Discovery, pp. 107–121. Physica, Berlin (1998)
    Google Scholar
  28. Zhang, L., Zhang, B.: The Quotient Space Theory of Problem Solving. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 11–15. Springer, Heidelberg (2003)
    Chapter Google Scholar
  29. Yao, Y.Y.: Information granulation and Rough Set Approximation. International Journal of Intelligence Systems 16, 87–104 (2001)
    Article MATH Google Scholar
  30. Yao, Y.Y., Yao, J.T.: Granular Computing as a Basis for Consistent Classification Problems. In: Proc. of PAKDD 2002 Workshop on Foundations of Data Mining, CIICM, Taiwan, pp. 101–106 (2002)
    Google Scholar
  31. Yao, Y.Y., Zhong, N.: Granular Computing Using Information Tables. In: Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds.) Data Mining, Rough Sets and Granular Computing, pp. 102–124. Physica, Berlin (2002)
    Google Scholar
  32. Yao, J.T., Yao, Y.Y.: Induction of Classification Rules by Granular Computing. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 175–182. Springer, Heidelberg (2002)
    Chapter Google Scholar
  33. Peters, J.F., Skowron, A., Suraj, Z., Borkowski, M., Rzasa, W.: Measures of Inclusion and closeness of Information Granules: A Rough Set Approach. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 300–307. Springer, Heidelberg (2002)
    Chapter Google Scholar
  34. 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
  35. Liu, Q.: Granules and Reasoning Based on Granular Computing. In: Chung, P.W.H., Hinde, C.J., Ali, M. (eds.) IEA/AIE 2003. LNCS(LNAI), vol. 2718, pp. 516–526. Springer, Heidelberg (2003)
    Chapter Google Scholar
  36. Liau, C.-J.: Many-Valued Dynamic Logic for Qualitative Decision Theory. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 294–303. Springer, Heidelberg (1999)
    Chapter Google Scholar
  37. Doherty, P., Lukaszewicz, W., Szalas, A.: Information Granules for Intelligent Knowledge Structures. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 405–412. Springer, Heidelberg (2003)
    Chapter Google Scholar
  38. Skowron, A., Stepaniuk, J., Peters, J.F.: Approximation of Information Granule Sets. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 65–72. Springer, Heidelberg (2001)
    Chapter Google Scholar
  39. Zadeh, L.A.: Information Granulation and Its Centrality. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 35–36. Springer, Heidelberg (1998)
    Chapter Google Scholar

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