Defuzzification of Periodic Membership Function on Circular Coordinates
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:68028", author = "Takashi Mitsuishi and Koji Saigusa", title = "Defuzzification of Periodic Membership Function on Circular Coordinates", abstract = "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 = "Defuzzification, periodic membership function, polar
coordinates transformation.", volume = "8", number = "10", pages = "1292-4", }
