eng Oriental Scientific Publishing Company Biomedical and Pharmacology Journal 0974-6242 2025-02-20 18 March Spl Edition 179 190 10.13005/bpj/3080 62821 article Rashmi Singh 1 Aryan Chaudhary 2 Samrat Ray 3 Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, India Chief Scientific Advisor, Bio Tech Sphere Research, Kolkata, West Bengal, India Dean and Head of International Relations, IIMS, Pune, India Integrating Artificial Intelligence (AI) in medical imaging has revolutionized diagnostics by enhancing accuracy and efficiency. However, challenges related to interpretability, domain shifts, and trust hinder clinical adoption. This study introduces a fuzzy set theoretic based framework to address these issues, focusing on real-world applications. We used aa case study, where fuzzy membership grades (ranging from 0.1 to 0.9) were employed to classify tumor pixels, with a threshold of 0.6 indicating higher likelihood. Weighted average defuzzification techniques were used to integrate parameters such as pixel intensity, grayscale, and texture coefficient. Results demonstrated that pixels exceeding the threshold consistently aligned with tumor regions, validating the framework's reliability. Additionally, we explored domain shifts through feature distribution analysis between source and target datasets, highlighting the need for adaptive models. This research emphasizes the role of fuzzy sets in improving interpretability and adaptability in clinical settings, contributing to AI's trustworthiness and clinical acceptance. https://biomedpharmajournal.org/vol18marchspledition/decoding-challenges-using-mathematics-of-fuzzy-theory-in-interpretability-shifts-adaptation-and-trust/ AI Adaptation Domain Shift Interpretability Medical Imaging Trustworthiness