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Short Remark on 3-Dimensional Game Method for Modelling

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Book cover Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives (IWIFSGN 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1081))

Abstract

The Game Method for Modelling (GMM) was introduced, developed and applied in some areas in the recent years, but in all cases it used a 2-dimensional grid of squares. Here, for the first time, we discuss the GMM over 3-dimensional grid of cubes.

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References

  1. Atanassov, K.: On a combinatorial game-method for modelling. Adv. Model. Anal. 19(2), 41–47 (1994)

    Google Scholar 

  2. Atanassov, K.: Application of a combinatorial game-method for modelling. Part. 1: combinatorial algorithms for solving variants of the Steiner-Rosenbaum’s problem. Adv. Model. Anal. 2(1/2), 23–29 (1998)

    Google Scholar 

  3. Atanassov, K.: Application of a combinatorial game-method for modelling. Part. 2: algorithms for grouping and transfering of points and a general algorithm. Adv. Model. Anal. 2(1/2), 31–38 (1998)

    Google Scholar 

  4. Atanassov, K.: Game Method for Modelling. Academic Publishing House, Sofia (2011). “Prof. M. Drinov”

    Google Scholar 

  5. Atanassov, K.: On game-method for modelling. Adv. Stud. Contemp. Math. 22(2), 189–207 (2012)

    MathSciNet  MATH  Google Scholar 

  6. Atanassov, K., Atanassova, L.: A game method for modelling. In: Antonov, L. (ed.) Third International School “Automation and Scientific Innstrumentation", Varna, pp. 229–232 (1984)

    Google Scholar 

  7. Atanassov, K., Atanassova, L., Sasselov, D.: On the combinatorial game-method for modelling in astronomy. Comput. Rend. Acad. Bulg. Sci. 47(9), 5–7 (1994)

    MATH  Google Scholar 

  8. Atanassov, K., Fidanova, S.: Representation of the ACO-algorithm by the game method for modelling. In: Annual of “Informatics" Section Union of Scientists in Bulgaria, vol. 4, pp. 62–67 (2011)

    Google Scholar 

  9. Atanassov, K., Sotirov, S.: Representation of the neural networks by the game method for modeling. Adv. Stud. Contemp. Math. 22(3), 347–354 (2012)

    MathSciNet  MATH  Google Scholar 

  10. Atanassov, K., Sotirova, E.: Game method for modelling interpretations of some stochastic processes. In: Proceedings of the Jangjeon Mathematical Society, vol. 15 (2012). (in press)

    Google Scholar 

  11. Atanassova, L., Atanassov, K.: Intuitionistic fuzzy interpretations of Conway’s game of life. In: Lecture Notes in Computer Science, vol. 6046, pp. 232-239. Springer, Berlin (2011)

    Google Scholar 

  12. Atanassova, L., Atanassov, K.: Intuitionistic fuzzy interpretations of Conway’s game of life. Part 2: topological transformations of the game field. In: Proceedings of the 2nd Workshop on Generalized Nets, Intuitionistic Fuzzy Sets and Knowledge Engineering, London, 9 July 2010, pp. 83–88 (2010)

    Google Scholar 

  13. Atanassova, L., Atanassov, K.: Intuitionistic fuzzy interpretations of Conway’s game of life. Part 3: Modal and extended modal transformations of the game field. In: Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, vol. I: Foundations, pp. 25–31. SRI Polush Academy of Sciences, Warsaw (2011)

    Google Scholar 

  14. Atanassova, L., Atanassov, K.: On a game-method for modelling with intuitionistic fuzzy estimations: Part 1. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7116, pp. 182–189 (2012)

    Google Scholar 

  15. Dobrinkova, N., Fidanova, S., Atanassov, K.: Game-method model for field fires. In: Lecture Notes in Computer Science, vol. 5910, pp. 173–179 (2010)

    Google Scholar 

  16. Gardner, M.: The Unexpected Hanging and Other Mathematical Diversions. Simon & Schuster, New York (1969)

    Google Scholar 

  17. Kuratovski, K.: Topology. Academic Press, New York (1966)

    Google Scholar 

  18. Otto, S., Day, T.: A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Princeton University Press, New Jersey (2007)

    Book  Google Scholar 

  19. Sotirova, E., Atanassov, K., Fidanova, S., Velizarova, E., Vassilev, P., Shannon, A.: Application of the game method for modelling the forest fire perimeter expansion. Part 1: a model fire intensity without effect of wind. In: IFAC Workshop on Dynamics and Control in Agriculture and Food Processing, Plovdiv, 13–16 June 2012, pp. 159–163 (2012)

    Google Scholar 

  20. Sotirova, E., Atanassov, K., Fidanova, S., Velizarova, E., Vassilev, P., Shannon, A.: Application of the game method for modelling the forest fire perimeter expansion. Part 2: a model fire intensity with effect of wind. In: IFAC Workshop on Dynamics and Control in Agriculture and Food Processing, Plovdiv, 13–16 June 2012, pp. 165–169 (2012)

    Google Scholar 

  21. Sotirova, E., Atanassov, K., Fidanova, S., Velizarova, E., Vassilev, P., Shannon, A.: Application of the game method for modelling the forest fire perimeter expansion. Part 3: a model of the forest fire speed propagation in different homogenous vegetation types. In: IFAC Workshop on Dynamics and Control in Agriculture and Food Processing, Plovdiv, 13–16 June 2012, pp. 171–174 (2012)

    Google Scholar 

  22. Sotirova, E., Dimitrov, D., Atanassov, K.: On some application of game-method for modelling. Part. 1: forest dynamics. In: Proceedings of the Jangjeon Mathematical Society, vol. 15, no. 2, pp. 115–123 (2012)

    Google Scholar 

  23. Sotirova, E., Dobrinkova, N., Atanassov, K.: On some application of game method for modelling. Part 2: development of forest fire. In: Proceedings of the Jangjeon Mathematical Society, vol. 15, pp. 335–342 (2012)

    Google Scholar 

  24. Sotirova, E., Sotirov, S., Dimitrov, A., Atanassov, K.: On some application of game method for modelling. Part 3: simulation of oil transformation in marine environment. In: Proceedings of the Jangjeon Mathematical Society, vol. 15 (2012). (in press)

    Google Scholar 

  25. Velten, K.: Mathematical Modeling and Simulation. Wiley-VCH Verlag GmbH & Co. KgaA, Weinheim (2009)

    MATH  Google Scholar 

  26. http://en.wikipedia.org/wiki/Conway

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Acknowledgments

This work was partially supported by the Bulgarian National Science Fund Project DN16/6, 2017 “Integrated approach for modeling of the forest fires spread”.

Author information

Authors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 2, 1113, Sofia, Bulgaria

    Lilija Atanassova

  2. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 105, 1113, Sofia, Bulgaria

    Krassimir Atanassov

  3. Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Nora Angelova

Authors
  1. Lilija Atanassova
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  2. Krassimir Atanassov
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  3. Nora Angelova
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Corresponding author

Correspondence to Krassimir Atanassov .

Editor information

Editors and Affiliations

  1. Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering, Sofia, Bulgaria

    Vassia Atanassova

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Andrzej Kaluszko

  5. WIT- Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

  6. Polish Acadamy of Sciences, Systems Research Institute, Warsaw, Poland

    Jan W. Owsinski

  7. Intelligent Systems Laboratory, Faculty of Technical Sciences, Bourgas, Bulgaria

    Sotir Sotirov

  8. Intelligent Systems Laboratory, Prof. Assen Zlatarov University, Burgas, Bulgaria

    Evdokia Sotirova

  9. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  10. Polish Academy of Sciences, Systems Research Institute, Warszawa, Poland

    Slawomir Zadrozny

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Atanassova, L., Atanassov, K., Angelova, N. (2021). Short Remark on 3-Dimensional Game Method for Modelling. In: Atanassov, K., et al. Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives. IWIFSGN 2018. Advances in Intelligent Systems and Computing, vol 1081. Springer, Cham. https://doi.org/10.1007/978-3-030-47024-1_35

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