ALGORITHM FOR DETERMINING A STRONGLY CONNECTED FUZZY SET OF A PERIODIC FUZZY GRAPH
DOI:
https://doi.org/10.18522/2311-3103-2026-1-%25pKeywords:
Periodic fuzzy graph, reachability set, strongly connected fuzzy setAbstract
The article discusses a method for determining the strong connectivity of a periodic fuzzy graph (PFG), which can be used to make decisions in emergency situations such as evacuation. The concept of a fuzzy set of strong connectivity is introduced. The main attention is paid to the development of a method for finding a fuzzy set of strong connectivity, which makes it possible to determine the degree of reachability between the vertices of a graph in a certain number of time cycles. The paper begins with a review of existing approaches to connectivity analysis in fuzzy graphs, emphasizing the need to consider time and fuzzy parameters. The main part of the paper is devoted to the description of key concepts and definitions related to periodic fuzzy graphs. The concepts of fuzzy path, time and degree of reachability, as well as fuzzy set of reachability are introduced. An algorithm for finding a fuzzy set of reachability based on the wave method is proposed, which allows determining the degree and time of reachability between graph vertices. Next, the concept of fuzzy set of strong connectivity PFG is introduced and an algorithm for its determination is proposed. As an example, a specific PFG is considered for which the fuzzy set of strong connectivity is calculated. The proposed method can be useful for choosing a movement strategy during evacuation, especially in conditions where the territory model is represented by a periodic fuzzy graph. In the future, it is planned to explore issues related to finding a discrete-time reachability between vertices with a given degree of reachability
References
1. Nikashina P.O. Opredelenie maksimal'nogo potoka v nechetkom periodicheskom grafe [Determining the maximum flow in a fuzzy periodic graph], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engi-neering Sciences], 2024, No. 4 (240), pp. 31-40.
2. Nikashina P.O., Bozhenyuk A.V. Optimizatsiya transportnogo potoka na osnove periodicheskikh nechetkikh grafov [Optimization of traffic flow based on periodic fuzzy graphs], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2023, No. 4 (234), pp. 97-108.
3. Shaw D., Albores P., Anson S., Kailiponi P., Nagarajan M., Tissington P., and Hart T. Evacuation Responsiveness by Government Organisations (ERGO), Evacuation Preparedness Assessment Work-book. Technical report. Aston CRISIS Center, 2011.
4. Lumbroso D., and Vinet F. Tools to Improve the Production of Emergency Plans for Floods: Are They Being Used by the People that Need Them?, Journal of Contingencies and Crisis Management, 2012, Vol. 20, pp. 149-165.
5. Hissel M., François H., and Xiao J.J. Support for Preventive Mass Evacuation Planning in Urban Are-as, IET Conference Publications, 2011, 582, pp. 159-165.
6. Chiu Y., and Liu H.X. Emergency Evacuation, Dynamique Transportation Model, Spring Street, NY 10013, USA: Springer Science Buisiness Media, LLC, 2008.
7. Bayram V. Optimization models for large scale network evacuation planning and management: A litera-ture review, Surveys in Operations Research and Management Science, 2016, Vol. 21 (2), pp. 63-84.
8. Gao Z., Qu Y., Li X., Long J., and Huang H.-J. Simulating the dynamic escape process in large public places, Operations Research, 2014, Vol. 62 (6), pp. 1344-1357.
9. Lazo J.K., Waldman D.M., Morrow B.H., and Thacher J.A. Household evacuation decision making and the benefits of improved hurricane forecasting: Developing a framework for assessment, Weather and Forecasting, 2010, Vol. 25 (1), pp. 207-219.
10. Simonovic S.P., and Ahmad S. Computer-based model for flood evacuation emergency planning, Natu-ral hazards, 2005, Vol. 34 (1), pp. 25-51.
11. Dash N., and Gladwin H. Evacuation decision making and behavioral responses: Individual and house-hold, Natural Hazards Review, 2007, Vol. 8 (3), pp. 69-77.
12. Bozhenyuk A., Gorbachev S., and Knyazeva M. Finding Fuzzy Sets of Bases and Antibases of Periodic Fuzzy Graph, Lecture Notes in Networks and Systems (LNNS), 2024, Vol. 1089 (2), pp. 767-774.
13. Bozhenyuk A., Knyazeva M., Kosenko O., and Rozenberg I. Strong Connectivity Definition of Periodic Fuzzy Graph, Lecture Notes in Networks and Systems (LNNS), 2023, Vol. 758, pp. 168-174.
14. Lessan J., and Kim A.M. Planning evacuation orders under evacuee compliance uncertainty, Safety Sci-ence, 2022, 156, 105894.
15. Stepanov A., and Smith M.J. Multi-objective evacuation routing in transportation networks, European Journal of Operational Research, 2009, Vol. 198 (2), pp. 435-446.
16. Lindell M., and Prater C. Critical behavioral assumptions in evacuation time estimate analysis for private vehicles: Examples from hurricane research and planning, Journal of Urban Planning and Development, 2007, Vol. 133 (1), pp. 18-29.
17. Bretschneider S. Mathematical models for evacuation planning in urban areas, Lecture Notes in Econom-ics and Mathematical Systems, Vol. 659. Verlag Berlin Heidelberg, Springer, 2012.
18. Hissel F. Methodology for the implementation of mass evacuation plans, CEMEF, France, Compiègne, 2011.
19. Kailiponi P. Analyzing evacuation decision using Multi-Attribute Utility Theory (MAUT), Procedia Engineering, 2010, Vol. 3, pp. 163-174.
20. Regnier E. Public evacuation decision and hurricane track uncertainty, Management Science, 2008, Vol. 54 (1), pp. 16-28.
21. Agumya A., and Hunter G.J. Responding to the consequences of uncertainty in geographical data, Inter-national Journal of Geographical Information Science, 2002, Vol. 16 (5), pp. 405-417.
22. Kunz M., Gret-Regamey A., and Hurni L. Visualization of uncertainty in natural hazards assessments using an interactive cartographic information system, Natural Hazards, 2011, Vol. 59 (3), pp. 1735-1751.
23. Kacprzyk J., Zadrozny S., Nurmi H., and Bozhenyuk A. Towards Innovation Focused Fuzzy Decision Making by Consensus, In: Proceedings of IEEE Int. Conf. on Fuzzy Systems, 2021, pp. 256-268.
24. Bozhenyuk A., Gorbachev S., and Knyazeva M. Finding Fuzzy Sets of Bases and Antibases of Periodic Fuzzy Graph, Lecture Notes in Networks and Systems (LNNS), 2024, Vol. 1089 (2), pp. 767-774.
25. Bozhenyuk A., Knyazeva M., Kosenko O., and Rozenberg I. Strong Connectivity Definition of Periodic Fuzzy Graph, Lecture Notes in Networks and Systems (LNNS), 2023, Vol. 758, pp. 168-174
