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Singleton Representation of Fuzzy Set for Computing Fuzzy Model Response for Fuzzy Inputs

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Advances in Information Processing and Protection

Abstract

Classical fuzzy model computes a crisp response for crisp inputs. This paper presents a method for computing fuzzy model response for fuzzy inputs. The method is based on singleton representation of a fuzzy set and it enables to obtain fuzzy response for fuzzy inputs. The presented method is compared with alternative approaches: Zadeh’s possibilistic method and method based on similarity measure. The validity of the proposed method is illustrated with experimental results (in comparison with extension principle results).

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References

  1. Boukezzoula, R., Foulloy, L., Galichet, S.: Inverse Controller Design for Fuzzy Interval Systems. IEEE Trans. Fuzzy Syst. 14 (2006) 111–124

    Article  Google Scholar 

  2. Chen, S.-M., Yeh, M.-S., Hsiao, P.-Y.: A comparison of similarity measures of fuzzy values. Fuzzy Sets Syst. 72 (1995) 79-89

    Article  MathSciNet  Google Scholar 

  3. Fan, J., Xie, W.: Some notes on similarity measure and proximity measure. Fuzzy Sets Syst. 101 (1999) 403-412

    Article  MATH  MathSciNet  Google Scholar 

  4. Hanss, M.: Applied Fuzzy Arithmetic - An Introduction with Engineering Applications, Springer-Verlag, Berlin Heidelberg New York (2005)

    Google Scholar 

  5. Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: Theory and design. IEEE Trans. Fuzzy Syst. 8 (2000) 535-550

    Article  Google Scholar 

  6. Mamdani, E.H., Assilian, S.: An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. Int. J. Man-Machine Stud. 7 (1975) 1-13

    Article  MATH  Google Scholar 

  7. Murawko-Wiśniewska, K., Piegat, A.: The Structure of fuzzy model based on mixed data (In Polish). Roczniki Informatyki Stosowanej WI PS Nr 9 (2005) 107-113

    Google Scholar 

  8. Palm, R., Driankov, D.: Fuzzy inputs. Fuzzy Sets Syst. 70 (1995) 315-335

    Google Scholar 

  9. Pappis, C.P., Karacapilidis, N.I.: A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Syst. 56 (1993) 171-174

    Article  MATH  MathSciNet  Google Scholar 

  10. Pedrycz, W., Vasilakos, A.V.: Linguistic models and linguistic modeling. IEEE Trans. Syst., Man, Cybern. B. 29 (1999) 745-757

    Article  Google Scholar 

  11. Piegat, A.: Fuzzy modeling and control (In Polish). Akademicka Oficyna Wydawnicza EXIT, Warsaw, Poland (1999)

    Google Scholar 

  12. Rutkowski, L.: Methods and techniques of artificial intelligence (In Polish). Wydawnictwo Naukowe PWN, Warsaw, Poland (2005)

    Google Scholar 

  13. Wang, W.-J.: New similarity measures on fuzzy sets and on elements. Fuzzy Sets Syst. 85 (1997) 305-309

    Article  MATH  Google Scholar 

  14. Zadeh, L.A.: Fuzzy Sets. Inform. Control. 8 (1965) 338-353

    Article  MATH  MathSciNet  Google Scholar 

  15. Zadeh, L.A.: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Trans. Syst., Man and Cybern. 3 (1973) 28-44

    MATH  MathSciNet  Google Scholar 

  16. Zadeh, L.A.: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circuits Syst. 45 (1999) 105–119

    MathSciNet  Google Scholar 

  17. Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) – an outline. Information Sciences 172 (2005) 1-40

    Article  MATH  MathSciNet  Google Scholar 

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Murawko-Wiśniewska, K., Piegat, A. (2007). Singleton Representation of Fuzzy Set for Computing Fuzzy Model Response for Fuzzy Inputs. In: Pejaś, J., Saeed, K. (eds) Advances in Information Processing and Protection. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-73137-7_13

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  • DOI: https://doi.org/10.1007/978-0-387-73137-7_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-73136-0

  • Online ISBN: 978-0-387-73137-7

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