Complex Vague Graphs and Their Application in Decision-Making Problems

Fuzzy graph models are found everywhere in natural and human made structures, including process dynamics in biological, physical and social systems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A complex vague model is useful in the field of mathematics which gives more precision, comparability and flexibility to the system as compared to the vague model. In these years, a mathematical approach is a generalized approach of blending different aspects. According to the above mathematical approach, we investigate strong techniques which are based on complex vague graphs. The purpose of this research study is to present and explore the key properties including: Cartesian products, composition, strong product, semi-strong product and direct product of complex vague graphs with examples. Finally, we present application of complex vague graphs in decision-making problems.