Analysis of social networks and Wi-Fi networks by using the concept of picture fuzzy graphs

Atanassov’s intuitionistic fuzzy set described the uncertainty of real-life events with the help of a membership and a non-membership degree. However, human opinion cannot be restricted to yes or no, but there is some abstinence and refusal degree as well. In such cases, picture fuzzy set is a suitable solution which described the abstinence and refusal grade of human opinion along with membership and non-membership grades. The aim of this paper is to analyse a social network and a wife network using the concept of picture fuzzy graph (PFG). For this purpose, the concept of PFG is proposed and some basic terms are demonstrated including complement, degree and bridges. The main advantage of the proposed PFG is that it describes the uncertainty in any real-life event with the help of four membership degrees where the traditional FG and IFG fail to be applied. The viability of PFG is shown by utilizing the concept in demonstrating two real-life problems including a social network and a Wi-Fi-network. A comparison of PFG with existing notions is established showing its superiority over the existing frameworks.