Fuzzy Secure Double Resolving Set and Co-secure Double Resolving Set and its Application

Shanmugapriya R.; sangeetha P; Sivakumar T.

doi:10.5269/bspm.80061

Shanmugapriya R.
sangeetha P Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology
Sivakumar T.

Résumé

In this article, we present a novel concept in fuzzy graph theory named fuzzy secure double resolving set. The main contribution of this paper is the introduction of various fuzzy secure resolving sets such as fuzzy secure resolving set, fuzzy co-secure resolving set, fuzzy secure resolving number, fuzzy secure double resolving set, fuzzy co-secure double resolving set, fuzzy edge resolving set, fuzzy edge secure resolving set, fuzzy bi-resolving set, and fuzzy global resolving set. The primary contribution of this document is the implementation of the fuzzy secure double resolving set in uncertain graphs. It guarantees the identification and monitoring of nodes, even in the event of some node failures. This document defines fuzzy secure resolving set, examines its characteristics, and offers instances to illustrate its functional application. We additionally offer examples to assist in grasping how it functions. This idea is beneficial since it guarantees that even if certain nodes in the graph malfunction or cease to operate, the system is still capable of accurately identifying and monitoring other nodes. This is particularly beneficial for practical issues such as sensor networks, communication systems, and fields where high reliability is essential even in the presence of potential faults or unpredictability. We also present some properties, corollaries, results, and theorems related to fuzzy secure double resolving sets.

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