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Balanced Pythagorean Fuzzy Superhypergraphs with an Illustrative Application to Hypernetwork Modeling

Articles in Press

Document Type : Research Article

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

10.30473/coam.2026.77751.1406

Abstract

Complex hypernetworks are important in real-world problems, and their regularity and balance are particularly significant; hence, suitable mathematical tools are needed. In this regard, this paper introduces the notion of refined Pythagorean fuzzy superhypergraphs (RPFSs) on an arbitrary non-empty set, for the clustering of complex hypernetworks. We introduce the complement of an RPFS, classify RPFSs as complementary, self-complementary, complete, and regular, and investigate their fundamental properties. The notion of isomorphic RPFSs is established, which leads to self-complementary RPFSs, and conditions under which an RPFS is self-complementary are considered. For any RPFS, we introduce density measures for Pythagorean fuzzy links and Pythagorean fuzzy superedges, which serve as measures of coherence for hypernetworks, and we analyze these measures for constant complete and self-complementary RPFSs. The notions of Pythagorean fuzzy link-degree and superedge-degree are established, yielding positive regular hyperstructures whose densities are computed. Finally, balanced RPFSs are introduced, characterized via density, and analyzed under isomorphism.

Highlights

  1. Introduces balanced, refined Pythagorean fuzzy superhypergraphs (RPFS) via k-density.
  2. Defines complementary, complete, and c,c-constant RPFS with existence proofs.
  3. Establishes link-degree, superedge-degree, and r,s-regular RPFS constructions.
  4. Proves constant-complete RPFS are balanced and balance is isomorphism-invariant.
  5. Provides worked numerical examples illustrating density computations on small RPFS.

Keywords

Main Subjects

References
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Control and Optimization in Applied Mathematics

Articles in Press, Corrected Proof
Available Online from 26 September 2026
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