A Study on Optimizing the Maximal Product in Cubic Fuzzy Graphs for Multifaceted Applications

Abstract

Graphs in the field of science and technology make considerable use of theoretical concepts. When dealing with numerous links and circumstances in which there are varying degrees of ambiguity or robustness in the connections between aspects, rather than purely binary interactions, cubic fuzzy graphs (CFGs) are more adaptable and compatible than fuzzy graphs. To better represent the complexity of interactions or linkages in the real world, an emerging CFG can be very helpful in achieving better problem-solving abilities that specialize in domains like network analysis, the social sciences, information retrieval, and decision support systems. This idea can be used for a variety of uncertainty-related issues and assist decision-makers in selecting the best course of action through the use of a CFG. Enhancing the maximized network of three cubic fuzzy graphs’ decision-making efficiency was the ultimate objective of this study. We introduced the maximal product of three cubic fuzzy graphs to investigate how interval-valued fuzzy membership, fuzzy membership, and the miscellany of relations are all simultaneously supported through the aspect of degree and total degree of a vertex. Furthermore, the domination on the maximal product of three CFGs was illustrated to analyze the minimum domination number of the weighted CFG, and the proposed approach is illustrated with applications.