@article{Alharbi2025, 
author = {Hilah Awad Alharbi and Kholood Mohammad Alsager},
title = {Fermatean    m-polar fuzzy soft rough sets with application to medical diagnosis},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {6},
pages = {14314-14346},
keywords = {fermatean fuzzy set, m-polar fuzzy sets, soft rough set, decision making, coronary artery disease, uncertainty modeling, multi-criteria analysis, approximation spaces},
url = {https://www.sciopen.com/article/10.3934/math.2025645},
doi = {10.3934/math.2025645},
abstract = {In this work, we introduce the concept of new approximate fuzzy structures, specifically Fermatean    m-polar fuzzy soft rough sets (FMPFSRSs), a novel hybrid structure that combines soft sets, rough sets, Fermatean fuzzy sets, and    m-polar fuzzy sets. The proposed FMPFSRS model effectively captures data uncertainty and imprecision through crisp soft and Fermatean    m-polar fuzzy soft approximation spaces. We establish the fundamental properties of these approximation spaces (demonstrating 92% uncertainty reduction in test cases) and provide illustrative examples. Our medical case study on coronary artery disease diagnosis achieves 89.2% diagnostic accuracy, significantly outperforming traditional fuzzy set approaches (76.5% accuracy) while reducing decision time by 44% (2.3 sec vs 4.1 sec). The methodology classifies patients using multidimensional data analysis with score (   S  =  0.725 for severe cases), precision (   H  =  0.650), and certainty (   C  =  0.504) functions. Clinical validation shows strong parameter sensitivity (cholesterol    β  =  0.42,    p  <  0.001; blood pressure    β  =  0.38,    p  <  0.001), confirming the model's reliability. The framework's versatility is demonstrated through successful application to complex multi-criteria decision-making scenarios in healthcare, with particular effectiveness in handling cases showing 62% inherent data uncertainty.}
}