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International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(2): 93-104
Published online June 25, 2024
https://doi.org/10.5391/IJFIS.2024.24.2.93
© The Korean Institute of Intelligent Systems
Competitions on Fuzzy Mixed Graph and its Application in Countries for Health and Disaster
Pabitra Kumar Gouri1,2, Bharti Saxena1,2, Rajesh Kedarnath Navandar3, Pranoti Prashant Mane4, Ramakant Bhardwaj5, Jambi Ratna Raja Kumar6, Surendra Kisanrao Waghmare7, and Antonios Kalampakas8
1Department of Mathematics, Chhotakhelna Surendra Smriti Vidyamandir, Maligram, India
2Department of Mathematics, Rabindranath Tagore University, Bhopal, India
3Department of Electronic & Telecommunication Engineering, JSPM Jayawantrao Sawant College of Engineering Hadaspar, Pune, India
4Department of Computer Engineering, MES’s Wadia College of Engineering, Pune, India
5Department of Mathematics, Amity University, Kolkata, India
6Computer Engineering Department, Genba Sopanrao Moze College of Engineering, Pune, India
7Department of Electronics and Telecommunication Engineering, G H Raisoni College of Engineering and Management, Pune, India
8College of Engineering and Technology, American University of the Middle East, Egaila, Kuwait
Correspondence to :
Bharti Saxena (bhartisaxena060@gmail.com)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This study introduces the concept of fuzzy mixed graphs (FMGs) to represent uncertain relationships in social networks such as Facebook, where connections can be friends, followers, or mutuals. These graphs are an extension of the mixed graph theory, accommodating ambiguity in user relationships. We propose FMGs in which each vertex and link is assigned a membership degree between 0 and 1, reflecting the uncertainty of the connections. A subtype, competition FMGs, is explored to model scenarios in which users vie for shared resources or objectives. Our investigation reveals insights into the dynamics of competition within these graphs, including the conditions for the existence and uniqueness of maximal competitors, interplay between competition and network connectivity, and influence of fuzziness on competition intensity. By applying our theoretical framework to real-world scenarios, we demonstrate its utility in health and disaster management systems. By identifying essential regions and stakeholders affected by disease or disaster proliferation, our approach offers a novel analytical tool that can be substantiated by numerical simulations.
Keywords: Fuzzy mixed graphs, Social network analysis, Uncertainty modeling, Resource competition, Health systems analysis, Disaster management
Conflict of Interest
No potential conflict of interest relevant to this article was reported.
Biographies
E-mail : pabitrakumargouri@gmail.com
E-mail : bhartisaxena060@gmail.com
E-mail : navandarajesh@gmail.com
E-mail : ppranotimane@gmail.com
E-mail : rkbhardwaj100@gmail.com
E-mail : ratnaraj.jambi@gmail.com
E-mail : surendra.waghmare358@gmail.com, drssssamanta@gmail.com
E-mail : antonios.kalampakas@aum.edu.kw
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Original Article
International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(2): 93-104
Published online June 25, 2024 https://doi.org/10.5391/IJFIS.2024.24.2.93
Copyright © The Korean Institute of Intelligent Systems.
Competitions on Fuzzy Mixed Graph and its Application in Countries for Health and Disaster
Pabitra Kumar Gouri1,2, Bharti Saxena1,2, Rajesh Kedarnath Navandar3, Pranoti Prashant Mane4, Ramakant Bhardwaj5, Jambi Ratna Raja Kumar6, Surendra Kisanrao Waghmare7, and Antonios Kalampakas8
1Department of Mathematics, Chhotakhelna Surendra Smriti Vidyamandir, Maligram, India
2Department of Mathematics, Rabindranath Tagore University, Bhopal, India
3Department of Electronic & Telecommunication Engineering, JSPM Jayawantrao Sawant College of Engineering Hadaspar, Pune, India
4Department of Computer Engineering, MES’s Wadia College of Engineering, Pune, India
5Department of Mathematics, Amity University, Kolkata, India
6Computer Engineering Department, Genba Sopanrao Moze College of Engineering, Pune, India
7Department of Electronics and Telecommunication Engineering, G H Raisoni College of Engineering and Management, Pune, India
8College of Engineering and Technology, American University of the Middle East, Egaila, Kuwait
Correspondence to:Bharti Saxena (bhartisaxena060@gmail.com)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This study introduces the concept of fuzzy mixed graphs (FMGs) to represent uncertain relationships in social networks such as Facebook, where connections can be friends, followers, or mutuals. These graphs are an extension of the mixed graph theory, accommodating ambiguity in user relationships. We propose FMGs in which each vertex and link is assigned a membership degree between 0 and 1, reflecting the uncertainty of the connections. A subtype, competition FMGs, is explored to model scenarios in which users vie for shared resources or objectives. Our investigation reveals insights into the dynamics of competition within these graphs, including the conditions for the existence and uniqueness of maximal competitors, interplay between competition and network connectivity, and influence of fuzziness on competition intensity. By applying our theoretical framework to real-world scenarios, we demonstrate its utility in health and disaster management systems. By identifying essential regions and stakeholders affected by disease or disaster proliferation, our approach offers a novel analytical tool that can be substantiated by numerical simulations.
Keywords: Fuzzy mixed graphs, Social network analysis, Uncertainty modeling, Resource competition, Health systems analysis, Disaster management
Fig 1.
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Fuzzy mixed graph.
Fig 2.
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Flowchart for Algorithm 1.
Fig 3.
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Competition fuzzy graph.
Fig 4.
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Flowchart of Algorithm 2.
Fig 5.
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The 2-step competition fuzzy graph.
Fig 6.
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Competing countries.
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Table 1 . Collections of data on health and disasters of countries from Wikipedia.
Sl. No. Country name HI NHI DI NDI 1 Germany 73.32 0.894 2.95 0.444 2 India 67.13 0.819 6.64 1 3 The United Kingdom 74.46 0.908 3.54 0.533 4 France 79.99 0.976 2.62 0.395 5 Italy 66.59 0.812 4.42 0.666 6 Brazil 56.29 0.687 4.09 0.616 7 Canada 71.58 0.873 3.01 0.453 8 Russia 57.59 0.703 3.58 0.539 9 South Korea 81.97 1 4.59 0.691 10 Spain 78.88 0.962 3.05 0.459
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Table 2 . Competition for health.
1 2 3 4 5 6 7 8 9 10 1 0 0.075 0.014 0.082 0.082 0.207 0.021 0.191 0.106 0.039 2 0.075 0 0.089 0.157 0.007 0.132 0.054 0.116 0.181 0.036 3 0.014 0.089 0 0.068 0.096 0.221 0.035 0.205 0.092 0.053 4 0.082 0.157 0.068 0 0.164 0.289 0.103 0.273 0.024 0.121 5 0.082 0.007 0.096 0.164 0 0.125 0.061 0.109 0.188 0.043 6 0.207 0.132 0.221 0.289 0.125 0 0.186 0.016 0.313 0.168 7 0.021 0.054 0.035 0.103 0.061 0.186 0 0.17 0.127 0.018 8 0.191 0.116 0.205 0.273 0.109 0.016 0.17 0 0.297 0.152 9 0.106 0.181 0.092 0.024 0.188 0.313 0.127 0.297 0 0.145 10 0.068 0.143 0.054 0.014 0.15 0.275 0.089 0.259 0.038 0.107
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Table 3 . Competition for disaster.
1 2 3 4 5 6 7 8 9 10 1 0 0.556 0.089 0.049 0.222 0.172 0.009 0.095 0.247 0.015 2 0.556 0 0.467 0.605 0.334 0.384 0.547 0.461 0.309 0.541 3 0.089 0.467 0 0.138 0.133 0.083 0.08 0.006 0.158 0.074 4 0.049 0.605 0.138 0 0.271 0.221 0.058 0.144 0.296 0.064 5 0.222 0.334 0.133 0.271 0 0.05 0.213 0.127 0.025 0.207 6 0.172 0.384 0.083 0.221 0.05 0 0.163 0.077 0.075 0.157 7 0.009 0.547 0.08 0.058 0.213 0.163 0 0.086 0.238 0.006 8 0.095 0.461 0.006 0.144 0.127 0.077 0.086 0 0.152 0.08 9 0.247 0.309 0.158 0.296 0.025 0.075 0.238 0.152 0 0.232 10 0.015 0.541 0.074 0.064 0.207 0.157 0.006 0.08 0.232 0
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Table 4 . Resultant competition.
1 2 3 4 5 6 7 8 9 10 1 0 0.075 0.014 0.049 0.082 0.172 0.009 0.095 0.106 0.015 2 0.075 0 0.089 0.157 0.007 0.132 0.054 0.116 0.181 0.036 3 0.014 0.089 0 0.068 0.096 0.083 0.035 0.006 0.092 0.053 4 0.049 0.157 0.068 0 0.164 0.221 0.058 0.144 0.024 0.064 5 0.082 0.007 0.096 0.164 0 0.05 0.061 0.109 0.025 0.043 6 0.172 0.132 0.083 0.221 0.05 0 0.163 0.016 0.075 0.157 7 0.009 0.054 0.035 0.058 0.061 0.163 0 0.086 0.127 0.006 8 0.095 0.116 0.006 0.144 0.109 0.016 0.086 0 0.152 0.08 9 0.106 0.181 0.092 0.024 0.025 0.075 0.127 0.152 0 0.145 10 0.015 0.143 0.054 0.014 0.15 0.157 0.006 0.08 0.038 0
