On Fuzzy Sequences, Fixed Points and Periodicity in Iterated Fuzzy Maps

Horia Nicolai Teodorescu


I 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.


modeling, control, fuzzy map iteration, fuzzy sequence, behavior

Full Text:



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

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

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. Gökhan, and H. Altinok. On statistical convergence of vector-valued sequences associated with multiplier sequences. Ukrainian Mathematical Journal, Vol. 58, No. 1, 2006

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

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

DOI: https://doi.org/10.15837/ijccc.2011.4.2107

Copyright (c) 2017 Horia Nicolai Teodorescu

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.