Competitions on Fuzzy Mixed Graph and its Application in Countries for Health and Disaster

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.