Extended Bipolar Fuzzy Graph based Decision Making Systems and Their Applications

Abstract

Fuzzy graphs and their extensions have recently been utilized in complex decision-making problems to deal with uncertain situations in various fields including medicine, engineering, social sciences, etc. Multi-criteria decision-making models are significant tools for assessing various real-time problems by considering their diverse criteria. The utilization of fuzzy graphs provides an efficient outcome in handling complex decision-making problems. Real-world complex relations always require an opposite investigation to deal with the counter opinions. To tackle these issues, the bipolar fuzzy sets have been applied to the graph for defining the bipolar fuzzy graph. Building on these concepts, the proposed study investigates the bipolar fuzzy graphs and their extensions, presenting certain results and employing the extended bipolar fuzzy graphs in decision-making models to handle various complex problems. First, the best competitions and p-competitions among the vertices are defined in the bipolar fuzzy digraphs and their characterizations are derived with certain results. Also, the bipolar fuzzy decision making trail and evaluation laboratory and additive ratio assessment techniques are designed based on bipolar fuzzy graphs. Moreover, the notion of m-bipolar fuzzy preference relation and m-bipolar fuzzy preference relation graph are defined to examine the pairwise importance of the vertices in the m-bipolar fuzzy graphs. Also, the degree centrality of a vertex in the m-bipolar fuzzy graph is defined and employed to design a centrality based decision making technique under the m-bipolar fuzzy environment. Furthermore, dominating sets and various energy concepts are defined in a bipolar intuitionistic fuzzy environment with certain results and bounds. Finally, the bipolar intuitionistic fuzzy graph and its energy based decision-making systems are designed to show the applicability of the concepts. To illustrate the proposed ideas, various applications such as network selection, vaccine selection, healthcare waste