Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30523
Defuzzification of Periodic Membership Function on Circular Coordinates

Authors: Takashi Mitsuishi, Koji Saigusa


This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Keywords: periodic membership function, defuzzification, polar coordinates transformation

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1691


[1] L. A. Zadeh, "Fuzzy Sets,” Information and Control, Vol. 8, pp.338–353. 1965.
[2] L. A. Zadeh, "Fuzzy algorithms,” Information and Control, Vol. 12, pp.94–102, 1968.
[3] E. H. Mamdani, "Application of fuzzy algorithms for control of simple dynamic plant,” Proc. IEE 121, No. 12, pp.1585–1588, 1974.
[4] M. Mizumoto, "Improvement of fuzzy control (IV) - Case by product-sum-gravity method -,” Proc. 6th Fuzzy System Symposium, pp. 9–13, 1990.
[5] Werner Van Leekwijck and Etienne E. Kerre, "Defuzzification: criteria and classification,” Fuzzy Sets and Systems, vol. 108, pp. 159–178, 1999.
[6] Li Na and Weng Jing, "A New Defuzzification Method for Enhance Performance of Fuzzy Logic Control System”, Software Engineering and Knowledge Engineering: Theory and Practice, AISC 114 (2012) 403–409.
[7] Fabian C. Hadipriono and Kerning Sun, "Angular fuzzy set models for linguistic values,” Civil Engineering Systems, Volume 7, Issue 3, pp. 148–156, 1990.
[8] Kerning Sun, "Motion control using angular fuzzy set model,” Proceedings of 1993 Asia-Pacific Workshop on Advances in Motion Control , pp. 241–246, 1993.
[9] T. Mitsuishi, K. Wasaki and Y. Shidama, "Continuity of Fuzzy Controller” MECHANIZED MATHEMATICS AND ITS APPLICATIONS, Vol. 1, No. 1, pp.31–38, 2000.
[10] T. Mitsuishi, N. Kayaki, K. Saigusa, "Color construction using dual fuzzy system”, Proc. of IEEE International Symposium on Computational Intelligence for Measurement Systems and Applications (CIMSA), pp. 136–139, 2003.
[11] T. Mitsuishi, N. Kayaki, K. Saigu, M. Kochizawa, "Automatic Color Decision Using Fuzzy Control”, Proc. of IFAC Multitrack Conference on Advanced Control Strategies for Social and Economic Systems (ACS2004), Preprints Volume CD-ROM, 2004.
[12] T. Mitsuishi, M. Abe, K. Saigusa, N. Kayaki, M. Kochizawa, "Approximate Reasoning Using Fuzzy Set as Input Applied to Coloration”, Proc. of 2005 Asia-Pacific Workshop on Visual Information Processing, pp. 242–246, 2005.
[13] T. Mitsuishi, K. Saigusa and Y. Shidama, "Periodic Fuzzy Set on Circular Coordinates,” 6th Podlasie Conference on Mathematics (6PCM), pp. 68-70, 2014.