A multi-bipolar fuzzy graph and its centrality measure based decision making system for healthcare waste treatment method selection

Fuzzy graphs help to handle various real-life uncertain problems and fuzzy preference relations have widely been utilized to deal with various decision-making problems. In reality, the multi-dimensional and counter investigations of a problem always provide an efficient outcome. However, these conventional approaches often lack consideration of counter-views and multi-dimensional perspectives in problem-solving. Therefore, the present study defines the notion of multi-bipolar fuzzy preference relation to fuse the multi-dimensional and bipolar views in handling uncertain relations in real-time problems. The notion of multi-bipolar fuzzy preference relation graph is explored to effectively study the pairwise importance in terms of multi-bipolar fuzzy relations between the multi-bipolar fuzzy sets. Additionally, the concepts of degree, in-degree and out-degree centrality measures are explored within the multi-bipolar fuzzy graph context. On the other hand, these concepts are fused to design a multi-criteria decision-making technique, where the preference relation graph helps to analyze the pairwise importance among the criteria and in-degree centrality aids to consider the importance of a criteria from other criteria. Furthermore, this fusion is implemented to address the healthcare waste treatment selection problem, where steam sterilization and chemical disinfection resulted in first and last rank, respectively. For this problem, five alternatives and their ten essential criteria are considered from the view of technical, social, environmental and economic aspects. To demonstrate the superiority and validity of the proposed technique, a comparative study is performed with existing techniques. Finally, the stability of the results is analyzed through a sensitivity performance.