Decision-making methods based on fuzzy soft competition hypergraphs

Fuzzy soft set theory is an effective framework that is utilized to determine the uncertainty and plays a major role to identify vague objects in a parametric manner. The existing methods to discuss the competitive relations among objects have some limitations due to the existence of different types of uncertainties in a single mathematical structure. In this research article, we define a novel framework of fuzzy soft hypergraphs that export the qualities of fuzzy soft sets to hypergraphs. The effectiveness of competition methods is enhanced with the novel notion of fuzzy soft competition hypergraphs. We study certain types of fuzzy soft competition hypergraphs to illustrate different relations in a directed fuzzy soft network using the concepts of height, depth, union, and intersection simultaneously. We introduce the notions of fuzzy soft k-competition hypergraphs and fuzzy soft neighborhood hypergraphs. We design certain algorithms to compute the strength of competition in fuzzy soft directed graphs that reduce the calculation complexity of existing fuzzy-based non-parameterized models. We analyze the significance of our proposed theory with a decision-making problem. Finally, we present graphical, numerical, as well as theoretical comparison analysis with existing methods that endorse the applicability and advantages of our proposed approach.

Automated summary

Fuzzy soft set theory is used to identify uncertain and vague objects in a parametric manner. This research introduces the novel framework of fuzzy soft hypergraphs, which enhances the effectiveness of competition methods. Certain types of fuzzy soft competition hypergraphs are studied to illustrate different relations in a directed fuzzy soft network. Algorithms are designed to compute the strength of competition in fuzzy soft directed graphs, reducing the complexity of existing fuzzy-based non-parameterized models. The proposed theory is analyzed with a decision-making problem and compared with existing methods.