Granulation of Hypernetwork Models under the q -Rung Picture Fuzzy Environment

Anam Luqman, Muhammad Akram and Ali N. A. Koam
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Anam Luqman: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Muhammad Akram: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Ali N. A. Koam: Department of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan 45142, Saudi Arabia

Mathematics, 2019, vol. 7, issue 6, 1-25

Abstract: In this paper, we define q -rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q -rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q -rung picture fuzzy equivalence relation and q -rung picture fuzzy hierarchical quotient space structures. In particular, a q -rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q -rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q -rung picture fuzzy hypergraphs and the q -rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

Keywords: q-rung picture fuzzy set; q-rung picture fuzzy hypergraphs; granular computing; algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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