Complex Hesitant Fuzzy Graph

Government policymakers face a problem about illustrating and evaluating strategies and plan to design active communities which need to be assessed for studying the collaboration between ministries. This work aims at proposing a complex hesitant fuzzy graph that represents the collaboration and its factors between ministries. The present graph can transform complex information using two variables, which modify the consistency and performance of hesitant fuzzy graphs in representing information and the phases. The additional variable represents the phase/level/factors of information that may affect the meaning of the information. In addition, three types of products are defined between two complex hesitant fuzzy graphs. The vertex degrees of these new graphs are investigated and proved. Finally, the proposed graphs are illustrated by an application problem of evaluating the cooperation between ministries and inside one ministry to enhance the tool in representing two variables.