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Hexagonal Game Method model of forest fire spread with intuitionistic fuzzy estimations

Hexagonal Game Method model of forest fire spread with intuitionistic fuzzy estimations. Evdokia Sotirova Prof. Asen Zlatarov University, Burgas-8000, Bulgaria esotirova@btu.bg. Veselina Bureva Prof. Asen Zlatarov University, Burgas-8000, Bulgaria vesito_ka@abv.bg. Emilia Velizarova

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Hexagonal Game Method model of forest fire spread with intuitionistic fuzzy estimations

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  1. Hexagonal Game Method model of forest fire spreadwith intuitionistic fuzzy estimations Evdokia Sotirova Prof. Asen Zlatarov University, Burgas-8000, Bulgaria esotirova@btu.bg Veselina Bureva Prof. Asen Zlatarov University, Burgas-8000, Bulgaria vesito_ka@abv.bg Emilia Velizarova FRI - BAS, St. Kl. Ohridski Blvd. 132, 1756 Sofia, Bulgaria velizars@abv.bg Stefka Fidanova IICT - BAS Acad. G. Bonchev str. bl25A, 1113 Sofia, Bulgaria stefka@parallel.bas.bg Pencho Marinov IICT - BAS Acad. G. Bonchev str. bl25A, 1113 Sofia, Bulgaria pencho@parallel.bas.bg Krassimir Atanassov IBPhBME – BAS Sofia 1113, Bulgaria krat@bas.bg Anthony Shannon University of Technology Sydney, Australia tshannon38@gmail.com 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  2. Game Method for Modeling • Conway's Game of Life, CGL (infinite two-dimensional orthogonal grid of square cells) • Game Method for Modeling, GMM - one of the modifications of the CGL 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  3. Game Method for Modeling • We use: • set of symbols S; • n-dimensional simplex comprising of n-dimensional cubes (when n = 2, a two-dimensional grid of squares). • We assume that material points (objects) can be found in some of the centers of the n-dimensional cells. • The GMM-grid can be either finite or infinite. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  4. Game Method for Modeling • For i-th dimension of the grid there is natural number gi that corresponds to the number of the sequential cells of the grid in the present dimension; • For finite n-dimensional GMM-grid - there is a vector <g1, g2, …, gn> of the lengths of its sides. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  5. Game Method for Modeling • Lets A is set of rules: 1. rules for the motion of the objects along the vertices of the simplex; 2. rules for the interactions among the objects, e.g., when they are collected in one cell. • Let the rules from the i-th type be denoted as i-rules, where i= 1, 2. • When S = {*}, we obtain the standard CGL. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  6. Game Method for Modeling • Initial configuration - set of (ordered) (n+2)-tuples with an initial component being the number of the object; the second, third, etc. until the (n + 1)-st its coordinates; and the (n + 2)-nd its corresponding symbol from S. • Final configuration - the ordered set of (n+2)-tuples having the above form and being a result of the modifications that occurred during a certain number of applications of the rules from Aover a (fixed) initial configuration. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  7. Game Method for Modeling • The single application of a rule from A over a given configuration K is called an elementary step in the transformation of the model and is denoted by A1(K). • When we have some initial configuration, we obtain new configurations in a stepwise manner. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  8. R R 9 9 R 9 R R 9 9 9 R R 9 9 9 9 R 9 9 9 9 R 9 9 9 9 9 R 9 9 9 9 9 9 R 9 9 9 R 9 9 9 9 R 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 S 9 9 9 S S 9 9 9 9 9 S S 9 9 S S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 GMM-model of forest fire Finite grid, having the form of a hexagonal lattice, size 11x11; – river; – stones; – homogeneous forest (digits correspond to the wood mass per one unit square). R S 9 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  9. GMM-model of forest fire If some rule determines that symbol Y must be changed with symbol Z, let us denote this fact by Y Z. The fire will develop in concentric circles. Rules for decreasing the digits after the beginning of the fire: 1. R  R; 2. S  S; 3. 0  0; 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  10. GMM-model of forest fire 4. In the initial time-step, the fire starts from a fixed cell containing digit 9. On the second time-step, for the same cell 9  8. On the third time-step, for the same cell 8  7. In the same moment, all neighboring cells of the cell with the fire change their digits with the previous digit. 5. On the next time-steps, for the cells with fire 6. The process continues until all cells in the region contain only digit 0. In the opposite case, go to 5. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  11. Comparison of the models of the fire-processes in square and hexagonal lattices 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  12. Comparison of the models of the fire-processes in square and hexagonal lattices 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  13. Comparison of the models of the fire-processes in square and hexagonal lattices 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  14. Comparison of the models of the fire-processes in square and hexagonal lattices 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  15. Comparison of the models of the fire-processes in square and hexagonal lattices 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  16. Comparison of the models of the fire-processes in square and hexagonal lattices 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  17. Formulas intuitionistic fuzzy estimations for the areal of the fire 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  18. The values of functions (i), (i) and (i) 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  19. Conclusion • The hexagonal lattice presents in more realistic way the spread of the fire. • The intuitionistic fuzzy estimations for the areal of the fire were given. • In the next research we will model the fire-process in an inhomogeneous forest. • After that, the process will flow with existing of a wind. • Using the results of the model, we can check the development of a real forest fire, the occupation of new territories, the decrease in trees density, etc. 17th Int. Conf. on IFSs, Sofia, 1-2 November, 2013

  20. Acknowledgment The authors are grateful for the support provided by the project DFNI-I-01/0006 “Simulating the behaviour of forest and field fires”, funded by the National Science Fund, Bulgarian Ministry of Education, Youth and Science.

  21. Thank you for your attention!

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