Fuzzy approach for group decision-making in crisis situations
Abstract
The importance of correct and clear decisions during a complex and difficult situation is very easy to understand, but not so easy to achieve. Especially in situations where decision-makers must decide under time pressure and uncertainty. For instance, typical crisis situations have such characteristics. Given the uncertainty, subjectivity and ambiguity of human knowledge, crisis situations are also characterized by conflicting interests. In this article, we propose an approach based on fuzzy set theory to help decision-makers to find the collective decision considering weights of each member of the decision-making group. More specifically, the proposed approach uses new and innovative transformation of fuzzy numbers through α-level cuts. The key role in the transformation process is played by the shape and position of fuzzy numbers. Additionally, the Hamming distance will be used for the final interpretation of the results, in order to minimize the loss of information caused by defuzzification.
Keyword : α-level, group decision-making, fuzzy number, Hamming distance, linguistic scale, crisis
How to Cite
Škoda, M., Flegl, M., & Lozano, C. (2021). Fuzzy approach for group decision-making in crisis situations. Business: Theory and Practice, 22(1), 180-189. https://doi.org/10.3846/btp.2021.12148
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Buckley, J. J., Eslami, E., & Feuring, T. (2006). Fuzzy mathematics in economics and engineering. Physica-Verlag Publishing.
Burnett, J. J. (1998). A strategic approach to managing crises. Public Relations Review, 24(4), 475–488. https://doi.org/10.1016/S0363-8111(99)80112-X
Cabrerizo, F. J., Herrera-Viedma, E., & Pedrycz, W. (2013). A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. European Journal of Operational Research, 230(3), 624–633. https://doi.org/10.1016/j.ejor.2013.04.046
Carrasco, R., Villar, P., Hornos, M., & Herrera-Viedma, E. (2011). A linguistic multi-criteria decision making model applied to the integration of education questionnaires. International Journal of Computational Intelligence Systems, 4(5), 946−959. https://doi.org/10.2991/ijcis.2011.4.5.19
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Chen, S., & Hwang, C. (1992). Fuzzy multiple attribute decision making methods and applications. Springer. https://doi.org/10.1007/978-3-642-46768-4
Coombs, W. T., & Holladay, S. J. (2012). The handbook of crisis communication. Wiley-Blackwell.
Danielsson, E. (2016). Following routines: a challenge in crosssectorial collaboration. Journal of Contingencies and Crisis Management, 24(1), 36–45. https://doi.org/10.1111/1468-5973.12093
Doskočil, R. (2015). An evaluation of total project risk based on fuzzy logic. Business: Theory and Practice, 17(1), 23–31. https://doi.org/10.3846/btp.2016.534
Drakaki, M., Goren, H. G., & Tzionas, P. (2018). An intelligent multi-agent based decision support system for refugee settlement siting. International Journal of Disaster Risk Reduction, 31, 576–588. https://doi.org/10.1016/j.ijdrr.2018.06.013
Granot, H. (1997). Emergency inter‐organizational relationships. Disaster Prevention and Management: An International Journal, 6(5), 305–310. https://doi.org/10.1108/09653569710193736
Herrera, F., Alonso, S., Chiclana, F., & Herrera-Viedma, E. (2009). Computing with words in decision making: foundations, trends and prospects. Fuzzy Optimization and Decision Making, 8(4), 337–364. https://doi.org/10.1007/s10700-009-9065-2
Hodgett, R. E., & Siraj, S. (2019). SURE: A method for decision-making under uncertainty. Expert Systems with Applications, 115, 684–694. https://doi.org/10.1016/j.eswa.2018.08.048
Iliadis, L. (2005). A decision support system applying an integrated fuzzy model for long-term forest fire risk estimation. Environmental Modelling & Software, 20(5), 613–621. https://doi.org/10.1016/j.envsoft.2004.03.006
Ishizaka, A., & Nemery, P. (2013). Multi-criteria decision analysis: methods and software. Wiley. https://doi.org/10.1002/9781118644898
Jia, X., Morel, G., Martell-Flore, H., Hissel, F., & Batoz, J.-L. (2016). Fuzzy logic based decision support for mass evacuations of cities prone to coastal or river floods. Environmental Modelling & Software, 85, 1–10. https://doi.org/10.1016/j.envsoft.2016.07.018
Jiang, W., Deng, L., Chen, L., Wu, J., & Li, J. (2009). Risk assessment and validation of flood disaster based on fuzzy mathematics. Progress in Natural Science, 19(10), 1419–1425. https://doi.org/10.1016/j.pnsc.2008.12.010
Kailiponi, P. (2010). Analyzing evacuation decisions using multi-attribute utility theory (MAUT). Procedia Engineering, 3, 163–174. https://doi.org/10.1016/j.proeng.2010.07.016
Kalkman, J. P., Kerstholt, J. H., & Roelofs, M. (2018). Crisis response team decision-making as a bureau-political process. Journal of Contingencies and Crisis Management, 26(4), 480–490. https://doi.org/10.1111/1468-5973.12243
Klir, G. J., & Yuan, B. (2015). Fuzzy sets and fuzzy logic: theory and applications. Pearson.
Koksalmis, E., & Kabak, O. (2019). Deriving decision makers’ weights in group decision making: An overview of objective methods. Information Fusion, 49, 146–160. https://doi.org/10.1016/j.inffus.2018.11.009
Kolen, B., Kok, M., Helsloot, I., & Maaskant, B. (2013). Evacu-Aid: a probabilistic model to determine the expected loss of life for different mass evacuation strategies during flood threats. Risk Analysis, 33(7), 1312–1333. https://doi.org/10.1111/j.1539-6924.2012.01932.x
Li, Q. (2013). A novel Likert scale based on fuzzy sets theory. Expert Systems with Applications, 40(5), 1609–1618. https://doi.org/10.1016/j.eswa.2012.09.015
Lin, C.-J., & Wu, W.-W. (2008). A causal analytical method for group decision-making under fuzzy environment. Expert Systems with Applications, 34(1), 205–213. https://doi.org/10.1016/j.eswa.2006.08.012
Lubiano, M. A., Montenegro, M., Sinova, B., de la Rosa de Saa, S., & Gil, M. A. (2016). Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications. European Journal of Operational Research, 251(3), 918–929. https://doi.org/10.1016/j.ejor.2015.11.016
Lumbroso, D., & Vinet, F. (2012). 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, 20(3), 149–165. https://doi.org/10.1111/j.1468-5973.2012.00665.x
Lyu, H., Sun, W., Shen, S., & Zhou, A. (2020). Risk assessment using a new consulting process in fuzzy AHP. Journal of Construction Engineering and Management, 146(3), 04019112. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001757
Masoum, M. A. S., & Fuchs, E. F. (2015). Power quality in power systems and electrical machines. Academic Press.
Medasani, S., Kim, J., & Krishnapuram, R. (1998). An overview of membership function generation techniques for pattern recognition. International Journal of Approximate Reasoning, 19(3-4), 391–417. https://doi.org/10.1016/S0888-613X(98)10017-8
Megahed, S. M., & Hassan, M. F. (2000, February 15−17). Current advances in mechanical design and production Vii: proceedings of the Seventh Cairo University International Mdp Conference. Cairo-Egypt. Pergamon.
Mello, A. S., & Ruckes, M. E. (2006). Team Composition. The Journal of Business, 79(3), 1019–1039. https://doi.org/10.1086/500668
Mianabadi, H., & Afshar, A. (2008). A new method to evaluate weights of decision makers and its application in water resource management. In Proceedings of the 13th IWRA World Water Congress, Montpelier, France (pp. 1−10).
Moynihan, D. P. (2009). The network governance of crisis response: case studies of incident command systems. Journal of Public Administration Research and Theory, 19(4), 895–915. https://doi.org/10.1093/jopart/mun033
Nahmias, S. (1978). Fuzzy variables. Fuzzy Sets and Systems, 1(2), 97–110. https://doi.org/10.1016/0165-0114(78)90011-8
Nokhbatolfoghahaayee, H., Menhaj, M. B., & Shafiee, M. (2010). Fuzzy decision support system for crisis management with a new structure for decision making. Expert Systems with Applications, 37(5), 3545–3552. https://doi.org/10.1016/j.eswa.2009.10.011
Nowlis, S. M., Kahn, B. E., & Dhar, R. (2002). Coping with ambivalence: the effect of removing a neutral option on consumer attitude and preference judgments. Journal of Consumer Research, 29(3), 319–334. https://doi.org/10.1086/344431
Pamučar, D., Stević, Ž., & Sremac, S. (2018). A new model for determining weight coefficients of criteria in MCDM Models: Full Consistency Method (FUCOM). Symmetry, 10(9), 393. https://doi.org/10.3390/sym10090393
Ryjov, A. (2003). Fuzzy linguistic scales: definition, properties and applications. In Soft Computing in Measurement and Information Acquisition, 23–38. Springer. https://doi.org/10.1007/978-3-540-36216-6_3
Rosenthal, U., ‘t Hart, P., & Kouzmin, A. (1989). Coping with crises: the management of disasters, riots and terrorism. Australian Journal of Management, 16(1), 99–102. https://doi.org/10.1177/031289629101600108
Rosenthal, U., Hart, P. t.’, & Kouzmin, A. (1991). The bureaupolitics of crisis management. National Emergency Training Center. https://doi.org/10.1111/j.1467-9299.1991.tb00791.x
Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234–281. https://doi.org/10.1016/0022-2496(77)90033-5
Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill. https://doi.org/10.21236/ADA214804
Saaty, T. L. (1990). How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 48(1), 9–26. https://doi.org/10.1016/0377-2217(90)90057-I
Saaty, T. L., & Vargas, L. (1994). Fundamentals of decision making and priority theory with the analytic hierarchy process. RWS.
Sechilariu, M., & Locment, F. (2016). Urban Dc microgrid: intelligent control and power flow optimization. Butterworth-Heinemann.
Shallit, J. (2009). Hamming distance for conjugates. Discrete Mathematics, 309(12), 4197–4199. https://doi.org/10.1016/j.disc.2008.11.001
Užga-Rebrovs, O., & Kuļešova, G. (2017). Comparative analysis of fuzzy set defuzzification methods in the context of ecological risk assessment. Information Technology and Management Science, 20(1), 25−29. https://doi.org/10.1515/itms-2017-0004
Voskoglou, M. G. (2018). Application of fuzzy relation equations to student assessment. American Journal of Applied Mathematics and Statistics, 6(2), 67−71. https://doi.org/10.12691/ajams-6-2-5
Wang, G. A., Jiao, J., Abrahams, A. S., Fan, W., & Zhang, Z. (2013). ExpertRank: A topic-aware expert finding algorithm for online knowledge communities. Decision Support Systems, 54(3), 1442–1451. https://doi.org/10.1016/j.dss.2012.12.020
Wang, Y.-M., Yang, J.-B., Xu, D.-L., & Chin, K.-S. (2006). On the centroids of fuzzy numbers. Fuzzy Sets and Systems, 157(7), 919–926. https://doi.org/10.1016/j.fss.2005.11.006
Xu, Z. (2012). Linguistic decision making: Theory and methods. Springer. https://doi.org/10.1007/978-3-642-29440-2
Yu, C.-S. (2002). A GP-AHP method for solving group decisionmaking fuzzy AHP problems. Computers & Operations Research, 29(14), 1969–2001. https://doi.org/10.1016/S0305-0548(01)00068-5
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338−353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, R., Phillis, Y. A., & Kouikoglou, V. S. (2005). Fuzzy control of queuing systems. Springer.
Zhu, F., Zhong, P.-A., & Sun, Y. (2018). Multi-criteria group decision making under uncertainty: Application in reservoir flood control operation. Environmental Modelling & Software, 100, 236–251. https://doi.org/10.1016/j.envsoft.2017.11.032
Berlin, J. M., & Carlstrom, E. D. (2011). Why is collaboration minimised at the accident scene? Disaster Prevention and Management: An International Journal, 20(2), 159–171. https://doi.org/10.1108/09653561111126094
Bjorck, A. (2016). Crisis typologies revisited: an interdisciplinary approach. Central European Business Review, 5(3), 25–37. https://doi.org/10.18267/j.cebr.156
Boin, A., Hart, P. 't, Stern, E., & Sundelius, B. (2005). The politics of crisis management. Cambridge University Press. https://doi.org/10.1017/CBO9780511490880
Bojadziev, G., & Bojadziev, M. (2007). Fuzzy logic for business, finance, and management. In Advances in Fuzzy Systems – Applications and Theory, 23 (2nd ed.). World Scientific Publishing Company. https://doi.org/10.1142/6451
Buckley, J. J., Eslami, E., & Feuring, T. (2006). Fuzzy mathematics in economics and engineering. Physica-Verlag Publishing.
Burnett, J. J. (1998). A strategic approach to managing crises. Public Relations Review, 24(4), 475–488. https://doi.org/10.1016/S0363-8111(99)80112-X
Cabrerizo, F. J., Herrera-Viedma, E., & Pedrycz, W. (2013). A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. European Journal of Operational Research, 230(3), 624–633. https://doi.org/10.1016/j.ejor.2013.04.046
Carrasco, R., Villar, P., Hornos, M., & Herrera-Viedma, E. (2011). A linguistic multi-criteria decision making model applied to the integration of education questionnaires. International Journal of Computational Intelligence Systems, 4(5), 946−959. https://doi.org/10.2991/ijcis.2011.4.5.19
Chen, L., Huang, Y.-C., Bai, R.-Z., & Chen, A. (2017). Regional disaster risk evaluation of China based on the universal risk model. Natural Hazards, 89(2), 647–660. https://doi.org/10.1007/s11069-017-2984-2
Chen, S., & Hwang, C. (1992). Fuzzy multiple attribute decision making methods and applications. Springer. https://doi.org/10.1007/978-3-642-46768-4
Coombs, W. T., & Holladay, S. J. (2012). The handbook of crisis communication. Wiley-Blackwell.
Danielsson, E. (2016). Following routines: a challenge in crosssectorial collaboration. Journal of Contingencies and Crisis Management, 24(1), 36–45. https://doi.org/10.1111/1468-5973.12093
Doskočil, R. (2015). An evaluation of total project risk based on fuzzy logic. Business: Theory and Practice, 17(1), 23–31. https://doi.org/10.3846/btp.2016.534
Drakaki, M., Goren, H. G., & Tzionas, P. (2018). An intelligent multi-agent based decision support system for refugee settlement siting. International Journal of Disaster Risk Reduction, 31, 576–588. https://doi.org/10.1016/j.ijdrr.2018.06.013
Granot, H. (1997). Emergency inter‐organizational relationships. Disaster Prevention and Management: An International Journal, 6(5), 305–310. https://doi.org/10.1108/09653569710193736
Herrera, F., Alonso, S., Chiclana, F., & Herrera-Viedma, E. (2009). Computing with words in decision making: foundations, trends and prospects. Fuzzy Optimization and Decision Making, 8(4), 337–364. https://doi.org/10.1007/s10700-009-9065-2
Hodgett, R. E., & Siraj, S. (2019). SURE: A method for decision-making under uncertainty. Expert Systems with Applications, 115, 684–694. https://doi.org/10.1016/j.eswa.2018.08.048
Iliadis, L. (2005). A decision support system applying an integrated fuzzy model for long-term forest fire risk estimation. Environmental Modelling & Software, 20(5), 613–621. https://doi.org/10.1016/j.envsoft.2004.03.006
Ishizaka, A., & Nemery, P. (2013). Multi-criteria decision analysis: methods and software. Wiley. https://doi.org/10.1002/9781118644898
Jia, X., Morel, G., Martell-Flore, H., Hissel, F., & Batoz, J.-L. (2016). Fuzzy logic based decision support for mass evacuations of cities prone to coastal or river floods. Environmental Modelling & Software, 85, 1–10. https://doi.org/10.1016/j.envsoft.2016.07.018
Jiang, W., Deng, L., Chen, L., Wu, J., & Li, J. (2009). Risk assessment and validation of flood disaster based on fuzzy mathematics. Progress in Natural Science, 19(10), 1419–1425. https://doi.org/10.1016/j.pnsc.2008.12.010
Kailiponi, P. (2010). Analyzing evacuation decisions using multi-attribute utility theory (MAUT). Procedia Engineering, 3, 163–174. https://doi.org/10.1016/j.proeng.2010.07.016
Kalkman, J. P., Kerstholt, J. H., & Roelofs, M. (2018). Crisis response team decision-making as a bureau-political process. Journal of Contingencies and Crisis Management, 26(4), 480–490. https://doi.org/10.1111/1468-5973.12243
Klir, G. J., & Yuan, B. (2015). Fuzzy sets and fuzzy logic: theory and applications. Pearson.
Koksalmis, E., & Kabak, O. (2019). Deriving decision makers’ weights in group decision making: An overview of objective methods. Information Fusion, 49, 146–160. https://doi.org/10.1016/j.inffus.2018.11.009
Kolen, B., Kok, M., Helsloot, I., & Maaskant, B. (2013). Evacu-Aid: a probabilistic model to determine the expected loss of life for different mass evacuation strategies during flood threats. Risk Analysis, 33(7), 1312–1333. https://doi.org/10.1111/j.1539-6924.2012.01932.x
Li, Q. (2013). A novel Likert scale based on fuzzy sets theory. Expert Systems with Applications, 40(5), 1609–1618. https://doi.org/10.1016/j.eswa.2012.09.015
Lin, C.-J., & Wu, W.-W. (2008). A causal analytical method for group decision-making under fuzzy environment. Expert Systems with Applications, 34(1), 205–213. https://doi.org/10.1016/j.eswa.2006.08.012
Lubiano, M. A., Montenegro, M., Sinova, B., de la Rosa de Saa, S., & Gil, M. A. (2016). Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications. European Journal of Operational Research, 251(3), 918–929. https://doi.org/10.1016/j.ejor.2015.11.016
Lumbroso, D., & Vinet, F. (2012). 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, 20(3), 149–165. https://doi.org/10.1111/j.1468-5973.2012.00665.x
Lyu, H., Sun, W., Shen, S., & Zhou, A. (2020). Risk assessment using a new consulting process in fuzzy AHP. Journal of Construction Engineering and Management, 146(3), 04019112. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001757
Masoum, M. A. S., & Fuchs, E. F. (2015). Power quality in power systems and electrical machines. Academic Press.
Medasani, S., Kim, J., & Krishnapuram, R. (1998). An overview of membership function generation techniques for pattern recognition. International Journal of Approximate Reasoning, 19(3-4), 391–417. https://doi.org/10.1016/S0888-613X(98)10017-8
Megahed, S. M., & Hassan, M. F. (2000, February 15−17). Current advances in mechanical design and production Vii: proceedings of the Seventh Cairo University International Mdp Conference. Cairo-Egypt. Pergamon.
Mello, A. S., & Ruckes, M. E. (2006). Team Composition. The Journal of Business, 79(3), 1019–1039. https://doi.org/10.1086/500668
Mianabadi, H., & Afshar, A. (2008). A new method to evaluate weights of decision makers and its application in water resource management. In Proceedings of the 13th IWRA World Water Congress, Montpelier, France (pp. 1−10).
Moynihan, D. P. (2009). The network governance of crisis response: case studies of incident command systems. Journal of Public Administration Research and Theory, 19(4), 895–915. https://doi.org/10.1093/jopart/mun033
Nahmias, S. (1978). Fuzzy variables. Fuzzy Sets and Systems, 1(2), 97–110. https://doi.org/10.1016/0165-0114(78)90011-8
Nokhbatolfoghahaayee, H., Menhaj, M. B., & Shafiee, M. (2010). Fuzzy decision support system for crisis management with a new structure for decision making. Expert Systems with Applications, 37(5), 3545–3552. https://doi.org/10.1016/j.eswa.2009.10.011
Nowlis, S. M., Kahn, B. E., & Dhar, R. (2002). Coping with ambivalence: the effect of removing a neutral option on consumer attitude and preference judgments. Journal of Consumer Research, 29(3), 319–334. https://doi.org/10.1086/344431
Pamučar, D., Stević, Ž., & Sremac, S. (2018). A new model for determining weight coefficients of criteria in MCDM Models: Full Consistency Method (FUCOM). Symmetry, 10(9), 393. https://doi.org/10.3390/sym10090393
Ryjov, A. (2003). Fuzzy linguistic scales: definition, properties and applications. In Soft Computing in Measurement and Information Acquisition, 23–38. Springer. https://doi.org/10.1007/978-3-540-36216-6_3
Rosenthal, U., ‘t Hart, P., & Kouzmin, A. (1989). Coping with crises: the management of disasters, riots and terrorism. Australian Journal of Management, 16(1), 99–102. https://doi.org/10.1177/031289629101600108
Rosenthal, U., Hart, P. t.’, & Kouzmin, A. (1991). The bureaupolitics of crisis management. National Emergency Training Center. https://doi.org/10.1111/j.1467-9299.1991.tb00791.x
Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234–281. https://doi.org/10.1016/0022-2496(77)90033-5
Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill. https://doi.org/10.21236/ADA214804
Saaty, T. L. (1990). How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 48(1), 9–26. https://doi.org/10.1016/0377-2217(90)90057-I
Saaty, T. L., & Vargas, L. (1994). Fundamentals of decision making and priority theory with the analytic hierarchy process. RWS.
Sechilariu, M., & Locment, F. (2016). Urban Dc microgrid: intelligent control and power flow optimization. Butterworth-Heinemann.
Shallit, J. (2009). Hamming distance for conjugates. Discrete Mathematics, 309(12), 4197–4199. https://doi.org/10.1016/j.disc.2008.11.001
Užga-Rebrovs, O., & Kuļešova, G. (2017). Comparative analysis of fuzzy set defuzzification methods in the context of ecological risk assessment. Information Technology and Management Science, 20(1), 25−29. https://doi.org/10.1515/itms-2017-0004
Voskoglou, M. G. (2018). Application of fuzzy relation equations to student assessment. American Journal of Applied Mathematics and Statistics, 6(2), 67−71. https://doi.org/10.12691/ajams-6-2-5
Wang, G. A., Jiao, J., Abrahams, A. S., Fan, W., & Zhang, Z. (2013). ExpertRank: A topic-aware expert finding algorithm for online knowledge communities. Decision Support Systems, 54(3), 1442–1451. https://doi.org/10.1016/j.dss.2012.12.020
Wang, Y.-M., Yang, J.-B., Xu, D.-L., & Chin, K.-S. (2006). On the centroids of fuzzy numbers. Fuzzy Sets and Systems, 157(7), 919–926. https://doi.org/10.1016/j.fss.2005.11.006
Xu, Z. (2012). Linguistic decision making: Theory and methods. Springer. https://doi.org/10.1007/978-3-642-29440-2
Yu, C.-S. (2002). A GP-AHP method for solving group decisionmaking fuzzy AHP problems. Computers & Operations Research, 29(14), 1969–2001. https://doi.org/10.1016/S0305-0548(01)00068-5
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338−353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, R., Phillis, Y. A., & Kouikoglou, V. S. (2005). Fuzzy control of queuing systems. Springer.
Zhu, F., Zhong, P.-A., & Sun, Y. (2018). Multi-criteria group decision making under uncertainty: Application in reservoir flood control operation. Environmental Modelling & Software, 100, 236–251. https://doi.org/10.1016/j.envsoft.2017.11.032