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Defects in the Defuzzification of Periodic Membership Functions on Orthogonal Coordinates and a Solution

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Fuzzy Logic in Intelligent System Design (NAFIPS 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 648))

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Abstract

Some membership functions which are characteristic functions of fuzzy sets are periodic due to the properties of the constituent elements of the fuzzy sets. In this study, some defects in the defuzzification of periodic membership functions on orthogonal coordinates are shown. Also, a solution in which the periodic membership function is transformed into polar coordinates is proposed. Moreover, a new defuzzification method for periodic membership functions on polar coordinates is proposed.

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References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  2. Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller, Part II. IEEE Trans. Syst. Man Cybern. 20(2), 419–435 (1990)

    Article  MATH  Google Scholar 

  3. Shi, Y., Sen, P.C.: A new defuzzification method for fuzzy control of power converters. In: Proceedings of the 2000 IEEE Industry Applications Conference. 35th IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy, vol. 2, pp. 1202–1209 (2000)

    Google Scholar 

  4. Leekwijck, W.V., Kerre, E.E.: Defuzzification: criteria and classification. Fuzzy Sets Syst. 108(2), 159–178 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Stefanini, L., Sorini, L.: Fuzzy arithmetic with parametric LR fuzzy numbers. In: Proceedings of IFSA/EUSFLAT Conference, pp. 600–605 (2009)

    Google Scholar 

  6. Na, L., Jing, W.: A new defuzzification method for enhance performance of fuzzy logic control system. In: Software Engineering and Knowledge Engineering: Theory and Practice. AISC, vol. 114, pp. 403–409 (2012)

    Google Scholar 

  7. Mitsuishi, T., Kawabe, J., Wasaki, K., Shidama, Y.: Optimization of fuzzy feedback control determined by product-sum-gravity method. J. Nonlinear Convex Anal. 1(2), 201–211 (2000)

    MathSciNet  MATH  Google Scholar 

  8. Mitsuishi, T., Terashima, T., Shidama, Y.: Optimization of SIRMs fuzzy model using Łukasiewicz logic. In: Proceedings of the 19th International Conference on Neural Information Processing (ICONIP 2012), Part II. LNCS, vol. 7664, pp. 108–116. Springer, Heidelberg (2012)

    Google Scholar 

  9. Mitsuishi, T., Terashima, T., Saigusa, K., Shidama, Y.: Continuity of approximate reasoning with Łukasiewicz logic for optimization of fuzzy logic control. In: Proceedings of the IEEE 2nd International Conference on Control and Fault-Tolerant Systems (Systol13), pp. 832–836 (2013)

    Google Scholar 

  10. Grabowski, A., Mitsuishi, T.: Initial comparison of formal approaches to fuzzy and rough sets. In: Proceedings of the 14th International Conference on Artificial Intelligence and Soft Computing (ICAISC). LNCS, vol. 9119, pp. 160–171. Springer, Heidelberg (2015)

    Google Scholar 

  11. Grabowski, A., Mitsuishi, T.: Formalizing lattice-theoretical aspects of rough and fuzzy sets. In: Proceedings of 10th International Conference RSKT 2015, Held as Part of the International Joint Conference on Rough Sets (IJCRS). LNCS, vol. 9436, pp. 347–356. Springer, Heidelberg (2015)

    Google Scholar 

  12. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  13. Miller, R.K., Michel, A.N.: Ordinary Differential Equations. Academic Press, New York (1982)

    MATH  Google Scholar 

  14. Riesz, F., Nagy, B.S.: Functional Analysis. Dover Publications, New York (1990)

    MATH  Google Scholar 

  15. Dunford, N., Schwartz, J.T.: Linear Operators Part I: General Theory. Wiley, New York (1988)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Marketing and Distribution Sciences, Kobe, Japan

    Takashi Mitsuishi

Authors
  1. Takashi Mitsuishi
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Correspondence to Takashi Mitsuishi .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Reformat

  5. Laboratory of Computational Intelligence and Automation, University of Waterloo, Waterloo, Ontario, Canada

    William Melek

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Mitsuishi, T. (2018). Defects in the Defuzzification of Periodic Membership Functions on Orthogonal Coordinates and a Solution. In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds) Fuzzy Logic in Intelligent System Design. NAFIPS 2017. Advances in Intelligent Systems and Computing, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-67137-6_40

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  • DOI: https://doi.org/10.1007/978-3-319-67137-6_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67136-9

  • Online ISBN: 978-3-319-67137-6

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