Multi-Scale Node Ranking in Fuzzy Graphs under Edge Uncertainty

Authors

  • Manas Kumar Khatua * Department of Mathematics, Swami Vivekananda University, Barrackpore–Barasat Road, Telinipara, Malir Math, Bara Kanthalia, West Bengal 700121, India.
  • Subhabrata Mondal Department of Mathematics, Swami Vivekananda University, Barrackpore–Barasat Road, Telinipara, Malir Math, Bara Kanthalia,West Bengal 700121, India. https://orcid.org/0000-0002-8167-7026

https://doi.org/10.48314/tsc.v1i4.73

Abstract

Node ranking in a fuzzy graph should distinguish immediate interaction strength, global accessibility, influential neighbors, and uncertainty in elicited edge memberships. A multi-scale fuzzy node-ranking score is introduced for this purpose. The construction combines normalized fuzzy degree, max–min accessibility, neighborhood support, and an explicit reliability discount. Unlike a direct weighted sum, the geometric local–global core prevents a node from compensating an almost absent local or global component by a single large component. Automorphism invariance, boundedness, parameter monotonicity, and perturbation stability are established. A sufficient rank-stability condition is obtained: two nodes retain their order whenever their score gap exceeds the sum of their perturbation radii. A seven-node communication network is calculated in full. The example shows a stable leading pair, a genuine crossover produced by the local–global preference parameter, and the effect of uncertainty widths on rank confidence. The analysis identifies the structural reason for each ranking change.

Keywords:

Fuzzy graph, Node ranking, Max–min connectivity, Perturbation stability, Centrality, Sensitivity analysis

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Published

2025-12-10

Issue

Vol. 1 No. 4 (2025): Transactions on Soft Computing (TSC)

Section

Articles

License

Copyright (c) 2026 Transactions on Soft Computing

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Khatua, M. K. ., & Mondal, S. (2025). Multi-Scale Node Ranking in Fuzzy Graphs under Edge Uncertainty. Transactions on Soft Computing , 1(4), 238-246. https://doi.org/10.48314/tsc.v1i4.73