On Fuzzy Sequences, Fixed Points and Periodicity in Iterated Fuzzy Maps
Keywords:modeling, control, fuzzy map iteration, fuzzy sequence, behavior
AbstractI exemplify various elementary cases of fuzzy sequences and results related to the iteration of fuzzy mappings and to fuzzy logic systems (FLS). Several types of fuzzy logic system iterations are exemplified in relationship with oscillations in FLS and with the problem of stability in fuzzy logic control. I establish several conditions for fixed points and periodicity of the iterations based on fuzzy systems.
P.E. Kloeden, Chaotic iterations of fuzzy sets. Fuzzy Sets and Systems 42 (1991) Volume 42, Issue 1, 5 July 1991, Pages 37-42
H.N. Teodorescu: Fuzzy oscillators. In: H.N. Teodorescu (Editor): Fuzzy Signals and Systems(Proc. AMSE Int. Symposium on Fuzzy Signals and Systems, Cetinje, Yugoslavia, 3-5 Sept. 1990). AMSE Press, France, 1990
H.N. Teodorescu: Controlled Fuzzy Oscillators. in vol: Engineering (Editors: R. Lowen, M. Roubens). Proc 4th IFSA Congress, 1991, Brussels, pp. 211-214
H.N. Teodorescu: Chaotic fuzzy systems: a survey. In: H.N. Teodorescu (Ed): Fuzzy Systems and Signals, vol. 3 (Proc. AMSE Int. Symp. Fuzzy Signals and Systems, Warsaw, June 11-13, 1991). AMSE Press (France)
H.N. Teodorescu: Chaos in fuzzy systems and signals. Vol. Proceedings of the 2nd Int. Conf. on Fuzzy Logic and Neural Networks. Vol. 1., pp. 21-50 (Jono Printing Co., 1992, Iizuka, Japan)
H.N. Teodorescu: Verhulst-type fuzzy growth processes and chaos. Vol. Fuzzy Systems. Proc. ISKIT'92, Iizuka, 1992. pp. 21-28
T. Yamakawa, H.N. Teodorescu, E. Sofron, S. Pavel: Fuzzy models of mechanical phenomena exhibit chaotic behavior. Vol. Fuzzy Systems. Proc. ISKIT'92, Iizuka, 1992. pp. 29-32
H.N. Teodorescu, T. Yamakawa, F. Grigoras, S. Pavel: A hardware implementation of a chaotic fuzzy logic system. Vol. Fuzzy Systems. Proc. ISKIT'92, Iizuka, 1992. pp. 33-38
H.N. Teodorescu, T. Yamakawa, V. Belous, St. Suceveanu: Interpretation of neuro-fuzzy systems in models in management and creativity. Chaos generation. Fuzzy Economic Review. Nov. 1995 (No. 1), pp. 25-42
S. Tamilselvan, K. Vairamanickam, K. Chandrasekhara Rao, Generalized Fuzzy Sequence Spaces. Int. Journal of Math. Analysis, Vol. 4, 2010, no. 45, 2235 - 2242
B.C. Tripathy and A. J. Dutta, On fuzzy real-valued double sequence spaces, Soochow J. of Mathematics, Volume 32, No. 4, pp. 509-520, October 2006
B.C. Tripathy and A. J. Dutta, On fuzzy real-valued double sequence space . Mathematical and Computer Modelling 46 (2007) 1294-1299 http://dx.doi.org/10.1016/j.mcm.2007.01.006
K. Chandrasekhara Rao, V. Karunakaran and K. Vairamanickam, Some Theorems on Fuzzy Matrix Transformation, Int. J. of Math. Analysis, Vol. 4, 2010, no. 5, 243 - 248
B.C. Tripathy, A.J. Dutta, Bounded variation double sequence space of fuzzy real numbers. Computers and Mathematics with Applications. Vol. 59, Issue 2, Jan. 2010, pp. 1031-1037 http://dx.doi.org/10.1016/j.camwa.2009.09.006
B.C. Tripathy, B. Sarma, Statistically Convergent Difference Double Sequence Spaces. Acta Mathematica Sinica, English Series, May, 2008, Vol. 24, No. 5, pp. 737-742 (Springer-Verlag 2008)
B.C. Tripathy, Sabita Mahanta, On a class of difference sequences related to the space defined by Orlicz functions. Math. Slovaca 57 (2007), No. 2, 171-178
M. Et, A. GÃ¶khan, and H. Altinok. On statistical convergence of vector-valued sequences associated with multiplier sequences. Ukrainian Mathematical Journal, Vol. 58, No. 1, 2006 http://dx.doi.org/10.1007/s11253-006-0056-y
L. Cheng, G. Lin, Y. Lan and H. Liu, Measure theory of statistical convergence. Science in China Series A: Mathematics, Vol. 51, Number 12, 2285-2303, DOI: 10.1007/s11425-008- 0017-z
N. Subramanian, M. Basarir, The Orlicz Space of Entire Sequence of Fuzzy Numbers. Tamsui Oxford J. of Mathematical Sciences 24(1) (2008) 109-122
D. Li, A. Laurent, and P. Poncelet, Discovery of Unexpected Fuzzy Recurrence Behaviors in Sequence Databases. Int. J. of Computer Information Systems and Industrial Management Applications (IJCISIM). Vol. 2 (2010), pp. 279-288
Zhi-Qiang Liu, Leonard T. Bruton, James C. Bezdek, Fellow, IEEE, James M. Keller, Sandy Dance, Norman R. Bartley, and Cishen Zhang, Dynamic Image Sequence Analysis Using Fuzzy Measures. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 31, No. 4, August 2001 557
M. Gholizadeh, M. M. Pedram, J. Shanbehzadeh, Fuzzy Sequence Mining for Similar Mental Concepts. Proc. Int. Multi-Conf. IMECS 2011, March 16-18, Hong-Kong, pp. 362-367
Bill C.H. Chang, Saman K. Halgamuge, Approximate symbolic pattern matching for protein sequence data. International Journal of Approximate Reasoning 32 (2003) 171-186 http://dx.doi.org/10.1016/S0888-613X(02)00082-8
J.-Y. Dieulot, P. Borne, Inverse Fuzzy Sum-product Composition and its Application to Fuzzy Linguistic Modelling. Studies in Informatics and Control, Vol. 14, No. 2, 2005, pp. 73-78
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.