A Comprehensive Exploration of Rough Set and#918; Labeling Techniques for Unstructured Data

Abstract

This research delves into techniques for managing unstructured data using rough sets and newlinetheir graphical representation known as Rough graphs, constructed via Rough membership newlinefunctions. The study explores labeling methodologies across various types of rough graphs newlinegenerated through approximation processes. It examines the mathematical implications newlineof graceful labeling for different rough graph structures, including Path rough graphs, newlineCycle rough graphs, and Complete rough graphs, among others. Theoretical findings are newlineaccompanied by illustrative counterexamples to validate the results. newlineAt the core of rough set theory lies the Decision/Information system, prompting newlinean investigation into graphs derived from Information systems using rough membership newlinefunctions. A novel labeling technique, Rough and#950; -graceful labeling, is introduced and applied to newlinerough tree, rough star graph, and rough comb graph structures, supported by relevant theorems. newlineConcepts of odd vertex and even vertex and#950; -graceful labeling are also introduced and applied to newlinestandard rough graph variants. newlineAdditionally, the research proposes the Rough Membership Boundary (RMB) algorithm newlinefor unstructured Wireless Sensor Networks (WSNs) data. This algorithm utilizes rough newlinegraph structures derived from WSN information systems, employing rough and#950; -labeling and newlineenergy calculation to delineate boundaries and select optimal paths. Comparative analysis newlinedemonstrates the superiority of the RMB algorithm over existing techniques newline