Skip to main content
SpringerLink
Log in

Automatic Rule Generation for Cellular Automata Using Fuzzy Times Series Methods

  • Conference paper
  • First Online:
Intelligent Systems (BRACIS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13653))

Included in the following conference series:

  • 687 Accesses

Abstract

Computer simulation of land dynamics have been widely used for several proposes, for example in epidemiological models. Cellular Automata (CA) is one of the strategies capable of predicting future land states over time based on a set of transitional rules. Building this set is not a straightforward task. It may require technical knowledge about the process, through years of scientific research. If machine learning techniques are applied, there is still the challenge of finding the best set of hyperparameters. In this context, the main goal of this paper is presenting a different approach of CA transitional rules set construction, based exclusively on historical data of a phenomenon. A multivariate Fuzzy Time Series (FTS) model is applied to learn and represent the local rules of the automaton. Therefore, we combine FTS and CA into an integrated modeling technique. The proposed approach was able to predict future behavior of a CA, with errors around 12%, confirming the potential of FTS transitional rules for CA.

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. Supported by CNPq Grant 312991/2020-7 and FAPEMIG Grant no. APQ-01779-21.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kari, J.: Theory of cellular automata: a survey. Theor. Comput. Sci. 334(1), 3–33 (2005). https://doi.org/10.1016/j.tcs.2004.11.021. ISSN 0304-3975

    Article  MathSciNet  MATH  Google Scholar 

  2. Speller, T., Whitney, D., Crawley, E.: Using shape grammar to derive cellular automata rule patterns. Complex Syst. 17, 79 (2007)

    MathSciNet  MATH  Google Scholar 

  3. Hajela, P., Kim, B.: On the use of energy minimization for CA based analysis in elasticity. In: 2000 Proceedings of the 41st AIAA/ASME/ASCE/AHS SDM Meeting, Atlanta, GA (2000)

    Google Scholar 

  4. Koza, J., et al.: Genetic Programming III: Darwinian Invention and Problem Solving. Morgan Kaufmann Publishers, San Francisco (1999)

    MATH  Google Scholar 

  5. Schimit, P.H.T.: A model based on cellular automata to estimate the social isolation impact on COVID-19 spreading in Brazil. Comput. Methods Prog. Biomed. 200, 105832 (2021). https://doi.org/10.1016/j.cmpb.2020.105832. ISSN 0169-2607

    Article  Google Scholar 

  6. Slimi, R., El Yacoubi, S., Dumonteil, E., Gourbière, S.: A cellular automata model for Chagas disease. Appl. Math. Model. 33(2), 1072–1085 (2009). https://doi.org/10.1016/j.apm.2007.12.028. ISSN 0307-904X

    Article  MathSciNet  MATH  Google Scholar 

  7. Massahud, R.A.T.: Dengue propagation model using cellular automata. Master’s thesis. Federal University of Lavras, Lavras (2011)

    Google Scholar 

  8. Ghosh, P., et al.: Application of cellular automata and Markov-chain model in geospatial environmental modeling - a review. Remote Sens. Appl. Soc. Environ. 5, 64–77 (2017). https://doi.org/10.1016/j.rsase.2017.01.005. ISSN 2352-9385

    Article  Google Scholar 

  9. Dawn, P., Steven, M., Marco, J., Matthew, H., Peter, D.: multi-agent systems for the simulation of land-use and land-cover change: a review. Ann. Assoc. Am. Geogr. 93, 314–337 (2003). https://doi.org/10.1111/1467-8306.9302004

    Article  Google Scholar 

  10. Larissa, F., Gina, O., Luiz, M.: Multistage evolutionary strategies for adjusting a cellular automata-based epidemiological model, 466–473 (2021). https://doi.org/10.1109/CEC45853.2021.9504738

  11. Lynch, C.: Big data: how do your data grow? Nature 455(7209), 28–29 (2008)

    Article  Google Scholar 

  12. Bose M., Mali, K.: Designing fuzzy time series forecasting models: a survey. Int. J. Approx. Reason. 111, 78–99 (2019). https://doi.org/10.1016/j.ijar.2019.05.002. ISSN 0888–613X

  13. Burks, A.W.: Von neumann’s self-reproducing automata. Essay on Cellular Automata, pp. 3–64 (1966)

    Google Scholar 

  14. Singh, P.: A brief review of modeling approaches based on fuzzy time series. Inter. J. Mach. Learn. Cybern. 8(2), 397–420 (2015). https://doi.org/10.1007/s13042-015-0332-y

    Article  Google Scholar 

  15. Morettin, P.A., Toloi, C.M.D.C.: Time Series Analysis. Edgard Blucher (2004)

    Google Scholar 

  16. Ibrahim, N.F., Wang, X.: Decoding the sentiment dynamics of online retailing customers: time series analysis of social media. Comput. Human Behav. 96, 32–45 (2019). https://doi.org/10.1016/j.chb.2019.02.004. ISSN 0747-5632

    Article  Google Scholar 

  17. Balzter, H., Braun, P.W., Kohler, W.: Cellular automata models for vegetation dynamics. Ecol. Model. 107(2), 113–125 (1998). https://doi.org/10.1016/S0304-3800(97)00202-0. ISSN 0304-3800

    Article  Google Scholar 

  18. Liu, Y., Phinn, S.: Modeling urban development with cellular automata incorporating fuzzy-set approaches. Comput. Environ. Urban Syst. 27, 637–658 (2003). https://doi.org/10.1016/S0198-9715(02)00069-8

    Article  Google Scholar 

  19. Mantelas, L., Prastacos, P., Hatzichristos, T., Koutsopoulos, K.: Using fuzzy cellular automata to access and simulate urban growth. GeoJournal 77, 13–28 (2012). https://doi.org/10.1007/s10708-010-9372-8

    Article  Google Scholar 

  20. Zheng, Z., Huang, W., Li, S., Zeng, Y.: Forest fire spread simulating model using cellular automaton with extreme learning machine. Ecol. Model. 348, 33–43 (2017). https://doi.org/10.1016/j.ecolmodel.2016.12.022

    Article  Google Scholar 

  21. Czerniak, J., Zarzycki, H., Apiecionek, L., Palczewski, W., Kardasz, P.: A cellular automata-based simulation tool for real fire accident prevention. Math. Probl. Eng. 1–12(02), 2018 (2018). https://doi.org/10.1155/2018/3058241

    Article  Google Scholar 

  22. Chopard, B.: Cellular automata and lattice Boltzmann modeling of physical systems, pp. 287–331 (2012). https://doi.org/10.1007/978-3-540-92910-9_9. ISBN 978-3-540-92909-3

  23. Chopard, B., Dupuis, A., Masselot, A., Luthi, P.: Cellular automata and lattice Boltzmann techniques: an approach to model and simulate complex systems. Adv. Comp. Syst. (ACS) 05, 103–246 (2002). https://doi.org/10.1142/S0219525902000602

    Article  MathSciNet  MATH  Google Scholar 

  24. Tavares, L.D.: An urban traffic simulator based on cellular automata. Master’s thesis, Federal University of Minas Gerais, Minas Gerais, Brazil (2010)

    Google Scholar 

  25. Melotti, G.: Application of cellular automata in complex systems: a study of case in spreading epidemics. Master’s thesis, Federal University of Minas Gerais, Minas Gerais, Brazil (2009)

    Google Scholar 

  26. Cattaneo, G., Flocchini, P., Mauri, G., Vogliotti, C., Santoro, N.: Cellular automata in fuzzy backgrounds. Physica D: Nonlinear Phenom. 105(1), 105–120 (1997). https://doi.org/10.1016/S0167-2789(96)00233-3. ISSN 0167-2789

    Article  MathSciNet  MATH  Google Scholar 

  27. Bone, C., Dragicevic, S., Roberts, A.: A fuzzy-constrained cellular automata model of forest insect infestations. Ecol. Model. 192(1), 107–125 (2006)

    Article  Google Scholar 

  28. Liu, Y., Phinn, S.R.: Modelling urban development with cellular automata incorporating fuzzy-set approaches. Comput. Environ. Urban Syst. 27(6), 637–658 (2003)

    Article  Google Scholar 

  29. Praba, B., Saranya, R.: Fuzzy graph cellular automaton and it’s applications in parking recommendations. Math. Nat. Comput. 18(1), 147–162 (2022). https://doi.org/10.1142/S1793005722500089

    Article  Google Scholar 

  30. Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series - Part I. Fuzzy Sets Syst. 54(1), 1–9 (1993). https://doi.org/10.1016/0165-0114(93)90355-L. ISSN 0165-0114

    Article  Google Scholar 

  31. Song, Q.: Seasonal forecasting in fuzzy time series. Fuzzy Sets Syst. 107, 235–236 (1999). https://doi.org/10.1016/S0165-0114(98)00266-8

    Article  MathSciNet  MATH  Google Scholar 

  32. Huarng, K.H., Yu, H.K.: A type 2 fuzzy time series model for stock index forecasting. Phys. A 353, 445–462 (2005)

    Article  Google Scholar 

  33. Efendi, R., Ismail, Z., Deris, M.M.: A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand. Appl. Soft Comput. 28, 422–430 (2015)

    Article  Google Scholar 

  34. Efendi, R., Deris, M.M., Ismail, Z.: Implementation of fuzzy time series in forecasting of the non-stationary data. Int. J. Comput. Intel. Appl. 15, 1650009 (2016). https://doi.org/10.1142/S1469026816500097

    Article  Google Scholar 

  35. Yu, H.-K.: Weighted fuzzy time series models for TAIEX forecasting. Physica A: Stat. Mech. Appl. 349(3–4), 609–624 (2005). https://doi.org/10.1016/j.physa.2004.11.006. ISSN 0378-4371

    Article  Google Scholar 

  36. Ismail, Z., Efendi, R.: Enrollment forecasting based on modified weight fuzzy time series. J. Artif. Intell. 4(1), 110–118 (2011)

    Article  Google Scholar 

  37. Sadaei, H.J.: Improved models in fuzzy time series for forecasting. Ph.D. thesis, Universiti Teknologi Malaysia (2013)

    Google Scholar 

  38. Cheng, C.-H., Chen, T.-L., Chiang, C.-H.: Trend-weighted fuzzy time-series model for TAIEX forecasting. In: King, I., Wang, J., Chan, L.-W., Wang, D.L. (eds.) ICONIP 2006. LNCS, vol. 4234, pp. 469–477. Springer, Heidelberg (2006). https://doi.org/10.1007/11893295_52

    Chapter  Google Scholar 

  39. Silva, P.C., Sadaei, H.J., Ballini, R., Guimarães, F.G.: Probabilistic forecasting with fuzzy time series. IEEE Trans. Fuzzy Syst. 28, 1771–1784 (2019)

    Article  Google Scholar 

  40. Severiano, C.A., de Lima e Silva, P.C., Cohen, M.W., Guimarães, F.G.: Evolving fuzzy time series for spatio-temporal forecasting in renewable energy systems. Renew. Energy 171, 764–783 (2021). https://doi.org/10.1016/j.renene.2021.02.117. ISSN 0960–1481

  41. Silva, P., Lucas, P., Sadaei, H., Guimarães, F.: Distributed evolutionary hyperparameter optimization for fuzzy time series. IEEE Trans. Netw. Ser. Manage. 1. https://doi.org/10.1109/TNSM.2020.2980289

  42. Silva, P.C.L. et al.: pyFTS: fuzzy time series for python. Belo Horizonte (2018). https://doi.org/10.5281/zenodo.597359

Download references

Author information

Authors and Affiliations

  1. Machine Intelligence and Data Science (MINDS) Laboratory, Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG, 31270-901, Brazil

    Lucas Malacarne Astore & Frederico Gadelha Guimarães

  2. Federal Institute of Minas Gerais, Campus Sabará, IFMG, Belo Horizonte, Brazil

    Carlos Alberto Severiano Junior

Authors
  1. Lucas Malacarne Astore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frederico Gadelha Guimarães
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Carlos Alberto Severiano Junior
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lucas Malacarne Astore .

Editor information

Editors and Affiliations

  1. Federal University of Rio Grande do Norte, Natal, Brazil

    João Carlos Xavier-Junior

  2. Federal University of Bahia, Salvador, Brazil

    Ricardo Araújo Rios

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Astore, L.M., Guimarães, F.G., Junior, C.A.S. (2022). Automatic Rule Generation for Cellular Automata Using Fuzzy Times Series Methods. In: Xavier-Junior, J.C., Rios, R.A. (eds) Intelligent Systems. BRACIS 2022. Lecture Notes in Computer Science(), vol 13653. Springer, Cham. https://doi.org/10.1007/978-3-031-21686-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-21686-2_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21685-5

  • Online ISBN: 978-3-031-21686-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation