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Mathematics 2019, 7(1), 91; https://doi.org/10.3390/math7010091

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

1
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54590, Pakistan
*
Author to whom correspondence should be addressed.
Received: 29 November 2018 / Revised: 9 January 2019 / Accepted: 12 January 2019 / Published: 16 January 2019
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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. View Full-Text
Keywords: q-rung orthopair fuzzy competition graphs; q-rung orthopair fuzzy clique; competition number; m-step competition number; soil ecosystem q-rung orthopair fuzzy competition graphs; q-rung orthopair fuzzy clique; competition number; m-step competition number; soil ecosystem
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Habib, A.; Akram, M.; Farooq, A. q-Rung Orthopair Fuzzy Competition Graphs with Application in the Soil Ecosystem. Mathematics 2019, 7, 91.

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