Exploring Metric Dimension of Rough Graphs in Dimensionality Reduction

Abstract

Rough Set Theory provides a robust mathematical framework for handling uncertainties newlineand imprecision inherent in knowledge bases. This work introduces a novel methodology newlinefor constructing Rough Graphs through the utilization of Rough Membership Functions. newlineExtensive mathematical investigations have been conducted to analyze various facets of newlinethese Rough Graphs. The construction of Rough Graphs is explored through diverse newlineapproaches, including set approximations, neighborhood formulations, and membership newlinefunction definitions. A comprehensive examination of Rough Graphs is undertaken, newlineencompassing their development via rough approximations, distinct forms of neighborhoods, newlineand membership function characterizations. Furthermore, the concept of Rougn Metric is newlineintroduced for Rough Graphs, enabling the computation of reducts, which are essential for newlineattribute reduction and feature selection. The proposed Rough Metric Dimension offers a newlinepowerful tool for dimensionality reduction in data analysis tasks. To augment the performance newlineand accuracy of dimensionality reduction, the Rough Metric Dimension is hybridized with newlinethe Linear Discriminant Analysis (LDA) technique. This integrated approach leverages the newlinestrengths of both methodologies, yielding remarkable results surpassing existing techniques newlinein terms of dimensionality reduction capabilities. The research concludes that the novel newlineconcept of Rough Metric Dimension, coupled with the LDA technique, presents a compelling newlineand effective solution for handling uncertainties, imprecision, and dimensionality reduction newlinechallenges in knowledge-based systems and data analysis applications newline