q -Rung Orthopair Fuzzy Hypergraphs with Applications

Anam Luqman, Muhammad Akram and Ahmad N. Al-Kenani
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Anam Luqman: Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan
Muhammad Akram: Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan
Ahmad N. Al-Kenani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia

Mathematics, 2019, vol. 7, issue 3, 1-22

Abstract: The concept of q -rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q , q ≥ 1 . In this research study, we design a new framework for handling uncertain data by means of the combinative theory of q -rung orthopair fuzzy sets and hypergraphs. We define q -rung orthopair fuzzy hypergraphs to achieve the advantages of both theories. Further, we propose certain novel concepts, including adjacent levels of q -rung orthopair fuzzy hypergraphs, ( α , β ) -level hypergraphs, transversals, and minimal transversals of q -rung orthopair fuzzy hypergraphs. We present a brief comparison of our proposed model with other existing theories. Moreover, we implement some interesting concepts of q -rung orthopair fuzzy hypergraphs for decision-making to prove the effectiveness of our proposed model.

Keywords: q -rung orthopair fuzzy hypergraphs; transversals of q -rung orthopair fuzzy hypergraphs; comparison analysis; decision-making; algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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