Issue: 2025/Vol.35/No.1, Pages
THE LAPLACIAN ENERGY OF AN INTUITIONISTIC FUZZY ROUGH GRAPH AND ITS UTILISATION IN DECISION-MAKING
Shaik Noorjahan
, Shaik Sharief Basha
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: S. Noorjahan, S. S. Basha. The Laplacian energy of an intuitionistic fuzzy rough graph and its utilisation in decision-making. Operations Research and Decisions 2025: 35(1). DOI 10.37190/ord250104
Abstract
An intuitionistic fuzzy rough model is a hybrid model that combines intuitionistic fuzzy sets and rough sets, addressing soft computing and ambiguity. It uses lower and upper approximation spaces in various fields, including science, technology, database systems, computer networks, and expert system architecture. The matrix of adjacency of an intuitionistic fuzzy rough graph is described in the article. The matrix of adjacency also provides the upper and lower bounds for Laplacian energy. These are used to define the Laplacian energies of intuitionistic fuzzy rough graphs and the weight function of Laplacian energy within these graphs. The intuitionistic fuzzy rough preference relation method is used to process the intuitionistic fuzzy rough weighted average. This technique is applied in data visualizations, which make data understandable by displaying it in a graphical or pictorial style. It supports decision-making and provides factual justification. This approach benefits any field that needs creative methods for presenting large volumes of complex data. Modern computer graphics have significantly influenced visualization.
Keywords: Laplacian energy (LE), intuitionistic fuzzy rough graph (IFRG), data visualization, and decision-making
Received: 25 January 2024 Accepted: 5 December 2024
Published online: 8 February 2025