A neutrosophic clustering approach to handle recommendation uncertainty for gray sheep users

Recommender systems play a crucial role in reducing information overload by providing personalized suggestions based on user preferences. However, gray sheep users are individuals whose preferences are inconsistent or partially aligned with both majority and minority groups, overlooked by conventional collaborative filtering methods, resulting in inaccurate or inconsistent recommendations. To address this challenge, this paper introduces an uncertainty-aware integration framework for gray sheep users, combining neutrosophic k-means clustering with item-based collaborative filtering (IBCF). Neutrosophic logic is an extension of fuzzy logic that describes data using three membership degrees: truth (support), indeterminacy (uncertainty), and falsity (contradiction), allowing for the flexible and reliable identification of users with ambiguous or non-conforming behaviors. IBCF uses item similarity to generate customized recommendations in the high-indeterminacy (gray sheep) cluster, whereas standard item-based collaborative filtering is used to process mainstream users. The performance gains for the high-indeterminacy (gray sheep) cluster are the only focus of this study. Experimental evaluation on the MovieLens 100 K dataset demonstrates that the proposed model improves gray sheep user treatment significantly, achieving higher precision (88.70%), recall (90.90%), F1-score (89.79%), reduced error rates (MAE = 0.534, RMSE = 0.719) and accuracy (84.07%) presented as an additional indication. In addition, neutrosophic k-means is evaluated on Book-Crossing and Last.fm, demonstrating generalizability beyond movies. These results confirm that explicit uncertainty modeling within collaborative filtering architectures can improve the quality of identification and recommendations for gray sheep users, reaching out to a key segment of the user base that conventional techniques have neglected.