A Fuzzy Collaborative Approach for Online Product Recommendation and Display

Online retailers face a coupled recommendation-display decision: they must infer user preferences from sparse, attribute-level, and linguistically uncertain evaluations, and then allocate scarce display slots under conflicting user-utility and platform-revenue objectives. This study proposes a two-stage hybrid decision-support model. Stage I transforms linguistic evaluations, or normalized star ratings when ratings are numerical, into interval type-2 fuzzy sets. It then uses item- and user-based collaborative filtering to complete missing attribute ratings and applies TOPSIS to obtain interpretable product preference scores. Stage II embeds these scores in a bi-objective integer programming model that selects products, assigns display slots, and allocates impressions. A big-M mixed-integer linear reformulation and an equivalence lemma are provided to strengthen mathematical reliability. An illustrative example, comparative analysis, sensitivity analysis, and random-instance robustness analysis show that the proposed method can handle sparse uncertain evaluations and quantify the trade-off between recommendation relevance and platform income.