Fuzzy Forcing Set on Fuzzy Graphs

The investigation of impact of fuzzy sets on zero forcing set is the main aim of this paper. According to this, results lead us to a new concept which we introduce it as Fuzzy Zero Forcing Set (FZFS). We propose this concept and suggest a polynomial time algorithm to construct FZFS. Further more we compute the propagation time of FZFS on fuzzy graphs. This concept can be more efficient to model opinion formation problem and independent cascade models in social networks. Some examples are provided to illustrate constructing FZFS on special fuzzy graphs. Also, we utilize the FZFS in a social network to model opinion formation problem.

Keywords:

Zero forcing set , fuzzy graph , fuzzy zero forcing set