A novel approach to Fuzzy mixed graph structure with application towards trade relations between countries

Many of the phenomena around us are a combination of directed and undirected relationships between different subjects, which will be more complex despite the existence of multiple relationships between objects. For example, in business relations between countries and social networks, communication is sometimes one-way or two-way. Checking and processing such information is managed in mixed graphs. Previous research has been based on the assumption that there is a general relationship between all vertices in a mixed graph. In this article, a new framework for fuzzy information management is introduced by combining fuzzy mixed graph and graph structure along with mentioning its properties. The concept of connectedness has been considered as one of the topics in this study. In this regard, some of their properties were examined by introducing some basic concepts such as paths, cycles, bridges, and cut vertices. Also, some attributes such as degree, neighborhood, order and size are defined. The results showed that although there existed a close relationship between the fuzzy mixed graph structure and the graph structure, the existence of multiple and distinct relationships between the vertices has created new definitions of concepts. This change can be seen especially in the degree of nodes and neighborhoods. Finally, its application in the field of trade relations between countries is presented.