Abstract
Rough set theory and rough graphs are employed for data analysis. Rough graphs utilize approximations, and this paper presents a method for implementing rough graphs using rough membership functions and graph labeling for data structures and reduction. This paper proposes a rough graph labeling method, termed rough -labeling similarity graph, that utilizes a similarity measure for vertex and edge labeling. This method aims to minimize boundary regions in rough graphs and is applicable to wireless sensor networks (WSNs). In WSN, the proposed algorithms such as PSO-LSTM, COA-LSTM, LOA-LSTM integrates with rough set theory based rough -labeling for boundary region identification. The proposed method incorporates the membership functions encapsulates the rough labeling graphs for cluster boundary region identification for WSN. The cluster boundary for WSN is based on rough set membership and rough labelling is termed as rough set membership boundary region (RMB). RMB in WSN and implementation of proposed routing algorithm such as LOA-LSTM provides high throughput and energy saving when compared to existing cluster boundary structure methods such as Voronoi, Spectrum and Chain.
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