Fuzzy forcing set on fuzzy graphs: definition and its application in social networks

Zero forcing is a dynamic process on a graph for changing the color of every vertex to black in an efficient way. This concept is very useful to model opinion formation problem and independent cascade model in social networks. Many type of networks should be modeled by fuzzy graphs. So, we introduce a definition of fuzzy zero forcing set (fzfs) on fuzzy graph. Also, we propose an algorithm to construct fzfs and compute the propagation time of fzfs on fuzzy graphs. Some examples on special fuzzy graphs illustrate the fzfs. Also we utilize the fzfs in a social network to model opinion formation problem. AMS Classification: 05B30; 05B05.