Abstract
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.
Highlights
Graph theory serves as an exceptionally useful tool in solving combinatorial problems in different areas including geometry, algebra, number theory, capturing the image, clustering, networking, zoology, topology, and social systems
Fuzzy graph models are advantageous mathematical tools for treating the combinatorial problems of various domains encompassing research, optimization, The associate editor coordinating the review of this manuscript and approving it for publication was Muhammad Imran Tariq
The flexibility and comparability of complex fuzzy models are higher than fuzzy models
Summary
Graph theory serves as an exceptionally useful tool in solving combinatorial problems in different areas including geometry, algebra, number theory, capturing the image, clustering, networking, zoology, topology, and social systems. S. Zeng et al.: Complex Vague Graphs and Their Application in Decision-Making Problems interval-valued fuzzy graphs. In the subject of graph theory, the terms metric dimension, domination number, total domination number, and graph labeling have a vital importance in many real life field problems. This research study discusses the cartesian product, composition, strong product, semi-strong product and direct product of complex vague graphs in this article. We have discussed the interesting and useful application of a complex vague graph in decision-making problem. The final section of this article is a conclusion in which we give a direction of future work
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