Abstract
The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty, as compared to the Pythagorean fuzzy model. The aim of this paper is to present q-rung orthopair fuzzy competition graphs (q-ROFCGs) and their generalizations, including q-rung orthopair fuzzy k-competition graphs, p-competition q-rung orthopair fuzzy graphs and m-step q-rung orthopair fuzzy competition graphs with several important properties. The study proposes the novel concepts of q-rung orthopair fuzzy cliques and triangulated q-rung orthopair fuzzy graphs with real-life characterizations. In particular, the present work evolves the notion of competition number and m-step competition number of q-rung picture fuzzy graphs with algorithms and explores their bounds in connection with the size of the smallest q-rung orthopair fuzzy edge clique cover. In addition, an application is illustrated in the soil ecosystem with an algorithm to highlight the contributions of this research article in practical applications.
Highlights
Configurations of node connections take place in a wide diversity of applications
The contribution or this research article is restricted to q-ROFCGs but it introduces the concept of competition number and m-step competition number of q-rung orthopair fuzzy graphs along with two algorithms
intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs) are both a good way to deal with fuzzy information as pairs of disjoint sets, called orthopairs
Summary
Configurations of node connections take place in a wide diversity of applications. They may depict physical networks, such as electric circuits, roadways, and organic molecules. The IFS can translate the uncertainty associated with both phases of species at the same time with the restriction that their sum is less than or equal to one To relax this condition and enhance one’s capability to express this knowledge more precisely, this paper defines q-ROFCGs to deal with competitions in many fields. The contribution or this research article is restricted to q-ROFCGs but it introduces the concept of competition number and m-step competition number of q-rung orthopair fuzzy graphs along with two algorithms. The results show their connection with the size of smallest q-rung orthopair fuzzy edge clique cover as bounds. This work suggests a novel approach towards the soil ecosystem by exploring the strength of competition of bacteria with an algorithm
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