Integrating fuzzy metrics and negation operator in FCM algorithm via genetic algorithm for MRI image segmentation

In this study, we redefine FCM algorithm by integrating fuzzy set theory, fuzzy metrics, and Sugeno negation principles. This innovative approach overcomes the limitations inherent in conventional machine learning models, especially in situations characterized by uncertainty, noise, and ambiguity. Our model utilizes the membership degrees from fuzzy set theory, and transforms the concept of proximity defined by fuzzy metrics into a minimization problem. This transformation is achieved using a linguistic negation operator, which is crucial for optimizing FCM algorithm's objective function. A significant innovation in our research is the use of GA for optimizing parameters within the contexts of fuzzy metrics and Sugeno negation. The precise optimization capabilities of GA greatly enhance the sensitivity and adaptability of FCM algorithm, thereby improving overall performance. By leveraging the meticulous parameter adjustments provided by GA, our approach has shown superior results in practical applications, such as brain MRI image segmentation, surpassing traditional methods. Experimental results highlight the considerable enhancements our proposed FCM algorithms bring over existing methods across various performance metrics. In conclusion, this study makes a valuable addition to the field of fuzzy-based machine learning methodologies. It combines the optimization strength of GA with the flexible classification capabilities of fuzzy logic. The integration of Sugeno negation and fuzzy metrics not only improves the accuracy and precision of FCM algorithm but also provides significant benefits in handling complex and ambiguous datasets. This research signifies a major advance in machine learning and fuzzy logic, setting the stage for future applications and studies. © The Author(s) 2024.