q-Rung Orthopair Fuzzy Competition Graphs with Application in the Soil Ecosystem

Amna Habib · Muhammad Akram · Adeel Farooq

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Fuzzy and Soft Set Theory Advanced Graph Theory Research Advanced Algebra and Logic

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.

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References

1965Fuzzy sets 1986Intuitionistic fuzzy sets 2013Pythagorean Membership Grades in Multicriteria Decision Making 2013Pythagorean fuzzy subsets 2016Generalized Orthopair Fuzzy Sets 2013Pythagorean Membership Grades, Complex Numbers, and Decision Making 2017Some q-Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple-Attribute Decision Making 2018Another view on q-rung orthopair fuzzy sets

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