Distance-Based Robust Fuzzy Topological Mathematical Modelling for Spider Networks in Edge Detection Techniques

Abstract

Abstract:
Introduction: Topological indices are numerical numbers used to represent a graph and describe its characteristics. In this method to find the distance based fuzzy topological spider network and it is implemented in robust regression. It will give the new proposed robust fuzzy topological model (RFTM). This model connected with the concept of image processing specially in edge detection techniques and verify our proposed model performance.

Objectives: Distance-based fuzzy topological indices are widely used in chemistry for quantitatively describing molecular structure and correlating it with various physicochemical properties. These indices are derived from the molecular graph, where atoms are represented as nodes and bonds as edges. There are several distances based topological indices, as well as a diverse set of distance-based molecular structure descriptors. Structure-based topological descriptors of chemical networks allow us to predict physicochemical attributes and bioactivities of compounds using QSAR/QSPR approaches. Topological indices are numerical numbers used to represent a graph and describe its characteristics. A robust fuzzy graph is a concept that integrates the robustness of graph structures with the flexibility and uncertainty modelling provided by fuzzy graph theory. It is used in applications where the system's topology or relationships among elements (nodes) are prone to noise, uncertainty, or partial truth, and there is a need for a reliable representation and analysis despite these uncertainties.

Methods: To find the distance based fuzzy topological spider network and it is implemented in robust regression. It will give the new proposed robust fuzzy topological model (RFTM). This model connected with the concept of image processing specially in edge detection techniques and verify our proposed model performance.

Results: In this paper, we provide analytical formulas for the Szeged index, edge Szeged index, edge vertex Szeged index, and PI index of spider networks and Augmented spider networks. Our proposed result also used in the concept of edge detection techniques.

Conclusions: The discrete characteristics of spider networks and augmented spider networks are determined using distance-based topological indices. We determined the analytical formulations for Wiener, Szeged, and their numerous versions, as well as PI of spider networks and augmented spider networks. The approach we utilized to calculate the topological networks is useful for evaluating the topological indices of various interconnection networks.The proposed model RFTM perform well compared to existing model. Also, it is the maximum no of true edges detected and reduced the number of false edges. The TLS MATLAB toolbox was used to simulate the previously provided data. Depending on the sample size, the data is generated randomly. Furthermore, the threshold settings in the toolbox in the image are set to two.