A Relational Framework of Inclusion and Preference on Neutrosophic Fuzzy Sets for Decision Analysis

Decision-making problems frequently involve incomplete, ambiguous, and inconsistent information, requiring models capable of representing multiple forms of uncertainty. Although neutrosophic fuzzy sets provide a flexible framework through truth, indeterminacy, and falsity memberships, the inclusion and preference mechanisms in this setting have not yet been systematically integrated into a unified decision framework. This study develops a coherent neutrosophic fuzzy decision framework by combining inclusion semantics with preference reasoning. Three inclusion relations are formulated together with their associated operations and subsethood similarities, while a neutrosophic fuzzy preference relation with additive consistency is constructed to support reciprocal pairwise preference reasoning under uncertainty. These components are integrated into a unified multi-criteria decision-making procedure and evaluated through a real educational recommendation problem involving subject-group selection for high-school students. The main experiment achieves recommendation accuracies ranging from 80% to 85% across the four considered relation settings and shows competitive performance relative to the considered existing approaches. A systematic sensitivity analysis over consistency thresholds and adjustment budgets further indicates stable top-set recommendations across the investigated parameter configurations, although minor changes may occur in the complete ranking under more stringent consistency requirements. The study therefore provides a theoretical framework and an empirical basis for uncertainty-aware decision support in neutrosophic fuzzy environments.