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Similarity-Based Reasoning Fuzzy Systems and Universal Approximation

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Mathematics and Computing 2013

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 91))

Abstract

In this work, we show that fuzzy inference systems (FIS) based on similarity-based reasoning (SBR), where the modification function is a fuzzy implication, is a universal approximator under suitable conditions on the other components of the fuzzy system.

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References

  1. Baczyński, M., Jayaram, B.: Fuzzy Implications, Studies in Fuzziness and Soft Computing, vol. 231. Springer, Berlin (2008)

    Google Scholar 

  2. Bandler, W., Kohout, L.J.: Semantics of implication operators and fuzzy relational products. Int. J. Man Mach. Stud. 12(1), 89–116 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, S.M.: A new approach to handling fuzzy decision-making problems. In: IEEE Trans. Sys. Man Cybern. 18(6), 1012–1016 (1988)

    Google Scholar 

  4. Cross, V., Sudkamp, T.: Fuzzy implication and compatibility modification. In: IEEE International Conference on Fuzzy Systems, vol. 1, pp. 219–224 (1993)

    Google Scholar 

  5. Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Control, 2nd edn. Springer, UK (1996)

    Book  MATH  Google Scholar 

  6. Dubois, D., Prade, H.: The generalized modus ponens under sup-min composition—a theoretical study. Gupta, M.M., Kandel, A., Bandler, W., Kiszka, J.B. (Eds.), Approximate Reasoning in Expert Systems, Elsevier, North Holland, pp. 157–166 (1985)

    Google Scholar 

  7. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms, Trends in Logic, vol. 8. Kluwer Academic Publishers, Dordrecht (2000)

    Book  Google Scholar 

  8. Li, Y.M., Shi, Z.K., Li, Z.H.: Approximation theory of fuzzy systems based upon genuine many-valued implications: MIMO cases. Fuzzy Sets Syst. 130, 159–174 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Li, Y.M., Shi, Z.K., Li, Z.H.: Approximation theory of fuzzy systems based upon genuine many-valued implications: SISO cases. Fuzzy Sets Syst. 130, 147–157 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Magrez, P., Smets, P.: Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems. Int. J. Intell. Syst. 4(2), 181–200 (1989). doi:10.1002/int.4550040205

  11. Mandal, S., Jayaram, B.: Approximation capability of siso fuzzy relational inference systems based on fuzzy implications. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2013 (2013). doi:10.1109/FUZZ-IEEE.2013.6622438

  12. Morsi, N.N., Fahmy, A.A.: On generalized modus ponens with multiple rules and a residuated implication. Fuzzy Sets Syst. 129(2), 267–274 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Roychowdhury, S., Pedrycz, W.: A survey of defuzzification strategies. Int. J. Intell. Syst. 16(6), 679–695 (2001)

    Article  MATH  Google Scholar 

  14. Tikk, D., Kóczy, L.T., Gedeon, T.D.: A survey on universal approximation and its limits in soft computing techniques. Int. J. Approx. Reasoning 33(2), 185–202 (2003)

    Article  MATH  Google Scholar 

  15. Turksen, I., Zhong, Z.: An approximate analogical reasoning approach based on similarity measures. IEEE Trans. Syst. Man Cybern. 18(6), 1049–1056 (1988). doi:10.1109/21.23107

  16. Štěpnička, M., Baets, B.D.: Monotonicity of implicative fuzzy models. In: IEEE International Conference on Fuzzy Systems (2010). doi:10.1109/FUZZY.2010.5584142

  17. Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. SMC-3(1), 28–44 (1973)

    Google Scholar 

  18. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-III. Inf. Sci. 9, 43–80 (1975)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Balasubramaniam Jayaram .

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Mandal, S., Jayaram, B. (2014). Similarity-Based Reasoning Fuzzy Systems and Universal Approximation. In: Mohapatra, R., Giri, D., Saxena, P., Srivastava, P. (eds) Mathematics and Computing 2013. Springer Proceedings in Mathematics & Statistics, vol 91. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1952-1_14

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