Seidel Laplacian energy of bipolar fuzzy graphs and enhanced score functions for decision-making applications

Sivaranjani Krishnaraj; O.V. Shanmuga Sundaram; Prasantha Bharathi Dhandapani; Taha Radwan; Sivaranjani Krishnaraj; O.V. Shanmuga Sundaram; Prasantha Bharathi Dhandapani; Taha Radwan

doi:10.3934/math.2025758

AIMS Mathematics

2025, Volume 10, Issue 7: 16865-16888. doi: 10.3934/math.2025758

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Seidel Laplacian energy of bipolar fuzzy graphs and enhanced score functions for decision-making applications

1.
Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, Tamil Nadu, India
2.
Department of Mathematics, Sree Saraswathi Thyagaraja College, Pollachi, Coimbatore 642107, Tamil Nadu, India
3.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

Received: 24 May 2025 Revised: 05 July 2025 Accepted: 17 July 2025 Published: 28 July 2025
MSC : 68R10, 90B10, 05C72

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.
- bipolar fuzzy graph,
- fuzzy logic,
- energy of a graph,
- Seidel Laplacian energy,
- symmetry,
- computational analysis,
- decision making
Citation: Sivaranjani Krishnaraj, O.V. Shanmuga Sundaram, Prasantha Bharathi Dhandapani, Taha Radwan. Seidel Laplacian energy of bipolar fuzzy graphs and enhanced score functions for decision-making applications[J]. AIMS Mathematics, 2025, 10(7): 16865-16888. doi: 10.3934/math.2025758

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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.

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