@article{Krishnaraj2025, 
author = {Sivaranjani Krishnaraj and O.V. Shanmuga Sundaram and Prasantha Bharathi Dhandapani and Taha Radwan},
title = {Seidel Laplacian energy of bipolar fuzzy graphs and enhanced score functions for decision-making applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {16865-16888},
keywords = {bipolar fuzzy graph, fuzzy logic, energy of a graph, Seidel Laplacian energy, symmetry, computational analysis, decision making},
url = {https://www.sciopen.com/article/10.3934/math.2025758},
doi = {10.3934/math.2025758},
abstract = {Bipolar fuzzy sets (BPFs) provide a suitable framework for knowledge representation if some data contains imprecise and ambiguous information. In this manuscript, the lower and upper bounds of the Seidel Laplacian energy of a bipolar fuzzy graph were examined with suitable illustrative examples. Moreover, the energy of a bipolar fuzzy graph, the Laplacian energy of a bipolar fuzzy graph, and the Seidel Laplacian energy of a bipolar fuzzy graph were examined. Furthermore, to address complex multi-criteria decision-making (MCDM) problems involving uncertainty and bipolar information, we proposed novel score functions: The score function, improved score function, and double improved score function. These functions were demonstrated through examples to effectively handle ambiguity and duality in decision-makers' inputs represented via bipolar fuzzy sets.}
}