Fuzzy taste, coherence, and clarity indices for recommender systems: Axiomatic properties and cross-domain validation

For analysis, each (item, tag) pair is represented by a graded relevance value in [0,1], constituting a natural fuzzy substrate for recommender-systems analysis. By aggregating these scores over each user’s positively rated items we construct a fuzzy taste profile and define two primary indices: Fuzzy Taste Diversity (FTD), the normalised Shannon entropy of the mass-normalised profile, and Fuzzy Taste Coherence (FTC), the mean pairwise cosine similarity among the liked items’ tag signatures; a convex combination of the two yields a descriptive composite, Fuzzy Preference Clarity (FPC). Working in the tradition of the Cerioli–Zani, Cheli–Lemmi, and Betti–Verma fuzzy poverty frameworks, we validate the two primary indices against two property systems stated on their respective domains—the tag simplex for FTD, finite collections of item signatures for FTC—including a replacement-monotonicity property for FTC stated relative to the leave-one-out signature sum, a U-statistic consistency result, and a separate proposition for the composite; no uniqueness or representation claim is made. A closed-form identity reduces the per-user coherence cost from O ( | L u | 2 | T | ) to O ( | L u | | T | ) , permitting evaluation on the full filtered MovieLens-25M (160, 756 users) and Book Genome (83, 393 users) populations within minutes. Leakage-free leave-5-out experiments on 154, 043 and 83, 393 validation users show that FTC has a stable positive association with the performance of tag-based content recommenders in both domains—the tag-profile recommender’s NDCG@10 rises from 0.0003 to 0.046 across FTC deciles on MovieLens and from 0.012 to 0.091 on Book Genome—and that in both domains this association persists under controls for history length, item popularity, and total profile mass and under covariate-adjusted decile comparisons, and on MovieLens-25M also under a chronological hold-out and two further independent random splits. A rating-only matrix-factorisation baseline delimits the scope of the finding: FTC is a diagnostic of tag-based content predictability, not of recommender performance in general. On Book Genome, an FTC-thresholded rule that assigns each user to either the popularity or the content-based recommender improves held-out NDCG@10 by 23.2% over the better fixed choice between the two.