Abstract
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.
Highlights
Fuzzy set theory, initiated by Zadeh [1] in 1965, is a powerful approach to study partial existence of objects between absolute true and absolute false
We evaluate the strength of power of each news channel using FS common enemy hypergraph
If we see in FS common enemy hypergraph 16, there is a hyperedge {Fox News, Sky News, MSNBC} in CEH(−→G (w1)) which indicates that these are the only channels which compete for A6
Summary
Fuzzy set theory, initiated by Zadeh [1] in 1965, is a powerful approach to study partial existence of objects between absolute true and absolute false. This technique of fuzziness has numerous applications in wireless communication for selecting appropriate network, information technology, hydrocarbon industry for food safety and piping risk assess-. Maji et al [10] presented a hybrid technique by integrating soft sets with fuzzy sets, and studied the properties and applications of fuzzy soft sets. Certain operations and properties of soft graphs and fuzzy soft graphs were studied by Akram and Nawaz [18]
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