The proliferation of Internet of Things (IoT) devices has revolutionized various sectors by enabling real-time monitoring, data collection, and intelligent decision-making. However, the massive volume of data generated by these devices presents significant challenges for data processing and analysis. Intrusion Detection Systems (IDS) for IoT require efficient and accurate identification of malicious activities amidst vast amounts of data. Feature selection is a critical step in this process, aiming to identify the most relevant features that contribute to accurate intrusion detection, thus reducing computational complexity and improving model performance. Traditional Mutual Information-based Feature Selection (MIFS) methods face challenges when applied to IoT data due to their inherent noise, uncertainty, and imprecision. This study introduces a novel Fuzzy Mutual Information-based Feature Selection (Fuzzy-MIFS) method that integrates fuzzy logic with Gaussian membership functions to address these challenges. The proposed method enhances the robustness and effectiveness of the feature selection process, resulting in improved accuracy and efficiency of IDSs in IoT environments. Experimental results demonstrate that the Fuzzy-MIFS method consistently outperformed existing feature selection techniques across various neural network models, such as CNN, LSTM, and DBN, showcasing its superior performance in handling the complexities of IoT data. The results show that Fuzzy-MIFS increased the accuracy from 0.962 to 0.986 for CNN, from 0.96 to 0.968 for LSTM, and from 0.96 to 0.97 for DBN.