Spectral Intuitionistic Fuzzy Hypergraph Operators and Dominance Kernels for Resilient Discrete Network Design

Year : 2026 | Volume : 03 | Issue : 02 | Page : 41 48
By

Chethana N S,

Markala Karthik,

S. Vairachilai,

  1. Student, Department of Mathematics, Central University of Karnataka, Kalaburagi, Karnataka, India
  2. Assistant Professor, Department of Electrical and Electronics Engineering, SR University, Warangal, Telangana, India
  3. Associate Professor, School of Computer Science and Artificial Intelligence, SR University, Warangal, Telangana, India

Abstract

A new discrete-mathematical framework is developed for resilient network design on intuitionistic fuzzy hypergraphs, where uncertainty is explicitly represented through membership, non-membership, and hesitation degrees associated with both vertices and hyperedges. These three components are systematically integrated into an effective incidence operator that captures the underlying uncertain relationships within complex hypergraph structures. Based on this operator, both un-normalised and normalized Laplacian matrices are formulated to characterize the spectral properties and connectivity of intuitionistic fuzzy hypergraphs under uncertainty. To quantify network resilience, a novel dominance kernel is introduced, combining certainty-weighted coverage, uncovered hyperedge penalties, and fragility measures across uncertain graph cuts into a unified optimization criterion. The resulting optimization problem seeks a resilient dominating transversal that maximizes network robustness while satisfying budget limitations and spectral-connectivity constraints. Theoretical analysis establishes fundamental variational bounds for the proposed objective function and derives smooth relaxation formulations that facilitate efficient optimization. Furthermore, projected ascent update rules are obtained in closed form, providing a computationally tractable solution strategy with provable convergence characteristics under the proposed relaxation. A stylized eight-vertex communication backbone is presented as an illustrative case study to demonstrate the practical applicability of the framework. Experimental analysis shows that the proposed dominance-kernel objective consistently identifies resilient vertex subsets with stronger algebraic connectivity, improved uncertainty tolerance, and better structural robustness compared with conventional coverage-only baseline methods. By integrating operator theory, spectral graph analysis, optimization techniques, and intuitionistic fuzzy hypergraph modeling into a unified mathematical framework, this work contributes a rigorous theoretical extension of intuitionistic fuzzy hypergraph theory and provides a powerful foundation for resilient network design within the broader field of discrete mathematical systems research.

Keywords: : Intuitionistic fuzzy hypergraph; domination; laplacian; algebraic connectivity; discrete optimisation; resilient networks

[This article belongs to Recent Trends in Mathematics ]

How to cite this article: Chethana N S, Markala Karthik, S. Vairachilai. Spectral Intuitionistic Fuzzy Hypergraph Operators and Dominance Kernels for Resilient Discrete Network Design. Recent Trends in Mathematics. 2026; 03(02):41-48.
How to cite this URL: Chethana N S, Markala Karthik, S. Vairachilai. Spectral Intuitionistic Fuzzy Hypergraph Operators and Dominance Kernels for Resilient Discrete Network Design. Recent Trends in Mathematics. 2026; 03(02):41-48. Available from: https://journals.stmjournals.com/rtm/article=2026/view=252084

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Regular Issue Subscription Original Research
Volume 03
Issue 02
Received 14/03/2026
Accepted 24/07/2026
Published 10/08/2026
Publication Time 149 Days

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