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Background: Fuzzy Rule Interpolation

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Backward Fuzzy Rule Interpolation
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Abstract

Conventional fuzzy reasoning methods such as Mamdani (Int J Man Mach Stud:7, 1975, [1]) and TSK (Fuzzy Sets Syst 28:15–33, 1988, [2], IEEE Trans Syst Man Cybern 1:116–132, 1985, [3]) require that the rule bases are dense. That is, the input universe of discourse is covered completely by the rule base.

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References

  1. E.H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7 (1975)

    Google Scholar 

  2. M. Sugeno, G. Kang, Structure identification of fuzzy model. Fuzzy Sets Syst. 28(1), 15–33 (1988)

    Article  MathSciNet  Google Scholar 

  3. T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 1, 116–132 (1985)

    Article  Google Scholar 

  4. T. Takagi, M. Sugeno, Comparison of fuzzy reasoning methods. Fuzzy Sets Syst. 8(3), 253–283 (1982)

    Article  MathSciNet  Google Scholar 

  5. L. Koczy, K. Hirota, Approximate reasoning by linear rule interpolation and general approximation. Int. J. Approx. Reason. 9(3), 197–225 (1993)

    Article  MathSciNet  Google Scholar 

  6. L. Koczy, K. Hirota, Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases. Inf. Sci. 71(1–2), 169–201 (1993)

    Article  MathSciNet  Google Scholar 

  7. Z. Huang, Q. Shen, Fuzzy interpolative reasoning via scale and move transformations. IEEE Trans. Fuzzy Syst. 14(2), 340–359 (2006)

    Article  Google Scholar 

  8. L. Koczy, K. Hirota, Fuzzy interpolation and extrapolation: a practical approach. IEEE Trans. Fuzzy Syst. 16(1), 13–28 (2008)

    Article  Google Scholar 

  9. M. Mizumoto, H.-J. Zimmermann, Comparison of fuzzy reasoning methods. Fuzzy Sets Syst. 8(3), 253–283 (1982)

    Article  MathSciNet  Google Scholar 

  10. H. Nakanishi, I. Turksen, M. Sugeno, A review and comparison of six reasoning methods. Fuzzy Sets Syst. 57(3), 257–294 (1993)

    Article  MathSciNet  Google Scholar 

  11. S. Kovács, Similarity based control strategy reconfiguration by fuzzy reasoning and fuzzy automata, in Proceedings of the IEEE Annual Conference on Industrial Electronics Society, vol. 1 (2000), pp. 542–547

    Google Scholar 

  12. S. Kovács, L.T. Kóczy, Application of interpolation-based fuzzy logic reasoning in behaviour-based control structures, in Proceedings of International Conference on Fuzzy Systems, vol. 3 (2004), pp. 1543–1548

    Google Scholar 

  13. S. Kovics, Fuzzy reasoning and fuzzy automata in user adaptive emotional and information retrieval systems, in Proceedings of IEEE International Conference on Systems, Man and Cybernetics, vol. 7 (2002), p. 6

    Google Scholar 

  14. K. Balázs, J. Botzheim, L. T. Kóczy, Comparative investigation of various evolutionary and memetic algorithms, in Computational Intelligence in Engineering. (Springer, 2010), pp. 129–140

    Google Scholar 

  15. Z.C. Johanyák, R. Parthiban, G. Sekaran, Fuzzy modeling for an anaerobic tapered fluidized bed reactor. Sci. Bull. Politeh. Univ. Timis. Rom. Trans. Autom. Control Comput. Sci. 52(66), 67–72 (2007)

    Google Scholar 

  16. K.W. Wong, D. Tikk, T.D. Gedeon, L.T. Kóczy, Fuzzy rule interpolation for multidimensional input spaces with applications: a case study. IEEE Trans. Fuzzy Syst. 13(6), 809–819 (2005)

    Article  Google Scholar 

  17. K.W. Wong, T.D. Gedeon, Fuzzy rule interpolation for multidimensional input space with petroleum engineering application, in Proceedings of IFSA World Congress and 20th NAFIPS International Conference, vol. 4 (2001), pp. 2470–2475

    Google Scholar 

  18. P. Baranyi, L.T. Kóczy, T.D. Gedeon, A generalized concept for fuzzy rule interpolation. IEEE Trans. Fuzzy Syst. 12(6), 820–837 (2004)

    Article  Google Scholar 

  19. B. Bouchon-Meunier, R. Mesiar, C. Marsala, M. Rifqi, Compositional rule of inference as an analogical scheme. Fuzzy Sets Syst. 138(1), 53–65 (2003)

    Article  MathSciNet  Google Scholar 

  20. Z.C. Johanyák, S. Kovács, A brief survey and comparison on various interpolation based fuzzy reasoning methods. Acta Polytech. Hung. 3(1), 91–105 (2006)

    Google Scholar 

  21. L.T. Koczy, S. Kovács, Linearity and the cnf property in linear fuzzy rule interpolation, in Proceedings of the Third IEEE Conference on Fuzzy Systems, 1994. IEEE World Congress on Computational Intelligence. (IEEE, 1994), pp. 870–875

    Google Scholar 

  22. S. Yan, M. Mizumoto, W.Z. Qiao, Reasoning conditions on koczy’s interpolative reasoning method in sparse fuzzy rule bases. Fuzzy Sets Syst. 75(1), 63–71 (1995)

    Article  Google Scholar 

  23. S. Chen, Y. Chang, Fuzzy rule interpolation based on the ratio of fuzziness of interval type-2 fuzzy sets. Expert Syst. Appl. 38(10), 12 202–12 213 (2011)

    Google Scholar 

  24. L. Lee, S. Chen, Fuzzy interpolative reasoning using interval type-2 fuzzy sets. New Front. Appl. Artif. Intell. 5027, 92–101 (2008)

    Article  Google Scholar 

  25. D.T.I.J.L.K.P.V.B.M.T. Gedeon, Stability of interpolative fuzzy kh controllers. Fuzzy Sets Syst. 125(1), 105–119 (2002)

    Article  MathSciNet  Google Scholar 

  26. R.C. Lee, Fuzzy logic and the resolution principle. J. ACM (JACM) 19(1), 109–119 (1972)

    Article  MathSciNet  Google Scholar 

  27. J. Robinson, A machine-oriented logic based on the resolution principle. J. ACM (JACM) 12(1), 23–41 (1965)

    Article  MathSciNet  Google Scholar 

  28. Z. Shen, L. Ding, M. Mukaidono, Fuzzy resolution principle, in Proceedings of the Eighteenth International Symposium on Multiple-Valued Logic. (IEEE, 1988), pp. 210–215

    Google Scholar 

  29. L. Zadeh, Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  30. L. Koczy, K. Hirota, Fuzzy logic and approximate reasoning. Synthese 30(3–4), 407–428 (1975)

    Google Scholar 

  31. W. Hsiao, S. Chen, C. Lee, A new interpolative reasoning method in sparse rule-based systems. Fuzzy Sets Syst. 93(1), 17–22 (1998)

    Article  MathSciNet  Google Scholar 

  32. P. Baranyi, D. Tikk, T.D. Gedeon, L.T. Kóczy, \(\alpha \)-cut interpolation technique in the space of regular conclusion, in Proceedings of IEEE International Conference on Fuzzy Systems, vol. 1 (2000), pp. 478–482

    Google Scholar 

  33. P. Baranyi, D. Tikk, Y. Yam, L.T. Kóczy, L. Nadai, A new method for avoiding abnormal conclusion for \(\alpha \)-cut based rule interpolation, in Proceedings of IEEE International Conference on Fuzzy Systems, vol. 1 (1999), pp. 383–388

    Google Scholar 

  34. D. Tikk, P. Baranyi, Comprehensive analysis of a new fuzzy rule interpolation method. IEEE Trans. Fuzzy Syst. 8(3), 281–296 (2000)

    Article  Google Scholar 

  35. D. Tikk, P. Baranyi, T.D. Gedeon, L. Muresan, Generalization of the rule interpolation method resulting always in acceptable conclusion. Tatra Mt. Math. Publ 21, 73–91 (2001)

    MathSciNet  MATH  Google Scholar 

  36. D. Tikk, P. Baranyi, L.T. Kóczy, T.D. Gedeon, On a stable and always applicable interpolation method, in Proceedings of IEEE International Conference on Fuzzy Systems, vol. 2 (2000), pp. 1049–1051

    Google Scholar 

  37. D. Tikk, P. Baranyi, Y. Yam, L.T. Kóczy, On the preservation of piecewise linearity of a modified rule interpolation approach, in Proceedings of the EUROFUSE-SIC Conference (1999), pp. 550–555

    Google Scholar 

  38. L. Koczy, K. Hirota, Stability of a new interpolation method, in Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, vol. 3 (1999), pp. 7–9

    Google Scholar 

  39. Y. Yam, L. Kóczy, Representing membership functions as points in high-dimensional spaces for fuzzy interpolation and extrapolation. IEEE Trans. Fuzzy Syst. 8(6), 761–772 (2000)

    Article  Google Scholar 

  40. T.D.G.K.W. Wong, D. Tikk, An improved multidimensional \(\alpha \)-cut based fuzzy interpolation technique, Conf Artificial Intelligence in Science and Technology (AISAT’2000) (2000), pp. 29–32

    Google Scholar 

  41. L.T.K. Sz, Kovács, Application of an approximate fuzzy logic controller in an agv steering system, path tracking and collision avoidance strategy. Fuzzy Set Theory Appl. Tatra Mt. Math. Publ., Math. Inst. Slovak Acad. Sci. 16, 456–467 (1999)

    Google Scholar 

  42. T. Deng, Y. Chen, W. Xu, Q. Dai, A novel approach to fuzzy rough sets based on a fuzzy covering. Inf. Sci. 177(11), 2308–2326 (2007)

    Google Scholar 

  43. S. Chen, Y. Ko, Fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on \(\alpha \)-cuts and transformations techniques. IEEE Trans. Fuzzy Syst. 16(6), 1626–1648 (2008)

    Article  Google Scholar 

  44. L. Koczy, K. Hirota, Preserving piece-wise linearity in fuzzy interpolation, in Proceedings of IEEE International Conference on Fuzzy Systems (2009), pp. 575–580

    Google Scholar 

  45. S. Jenei, Interpolation and extrapolation of fuzzy quantities revisited—(i) an axiomatic approach. Soft. Comput. 5, 179–193 (2001)

    Article  Google Scholar 

  46. S. Jenei, E.-P. Klement, R. Konzel, Interpolation and extrapolation of fuzzy quantities-the multiple-dimensional case. Soft. Comput. 6(3–4), 258–270 (2002)

    Article  Google Scholar 

  47. L. Koczy, K. Hirota, Fuzzy rule interpolation based on polar cuts, in Computational Intelligence, Theory and Applications. (Springer, 2006), pp. 499–511

    Google Scholar 

  48. M.M.S. Yan, W.Z. Qiao, An improvement to kóczy and hirota’s interpolative reasoning in sparse fuzzy rule bases. Int. J. Approx. Reason. 15, 185–201 (1996)

    Article  Google Scholar 

  49. L. Ughetto, D. Dubois, H. Prade, Fuzzy interpolation by convex completion of sparse rule bases, in Proceedings of International Conference on Fuzzy Systems (2000), pp. 465–470

    Google Scholar 

  50. P. Baranyi, T.D. Gedeon, L.T. Kóczy, A general interpolation technique in fuzzy rule bases with arbitrary membership functions, in Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, vol. 1 (1996), pp. 510–515

    Google Scholar 

  51. L. Ding, Z. Shen, M. Mukaidono, Revision principle for approximate reasoning, based on linear revising method, in Proceedings of the 2nd International Conference on Fuzzy Logic and Neural Networks (1992), pp. 305–308

    Google Scholar 

  52. D. Tikk, Z. Csaba Johanyák, S. Kovács, K.W. Wong, Fuzzy rule interpolation and extrapolation techniques: criteria and evaluation guidelines. J. Adv. Comput. Intell. Intell. Inform. 15(3), 254–263 (2011)

    Article  Google Scholar 

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Correspondence to Shangzhu Jin .

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Jin, S., Shen, Q., Peng, J. (2019). Background: Fuzzy Rule Interpolation. In: Backward Fuzzy Rule Interpolation. Springer, Singapore. https://doi.org/10.1007/978-981-13-1654-8_2

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