<![CDATA[Selecting an appropriate research topic is a critical yet challenging task for mathematics students, often hindered by misalignment between student interests, academic competencies, and supervisor availability. Traditional recommendation systems fail to capture the inherent uncertainty and ambiguity in human preferences, leading to suboptimal topic matches and prolonged study durations. This paper develops a research topic recommendation system specifically designed for mathematics students using an innovative Picture Fuzzy Distance Measure (PFDM). The picture fuzzy approach was selected for its comprehensiveness and detail in decision-making. Unlike traditional binary or even intuitionistic fuzzy models, this approach uniquely and simultaneously accommodates three degrees of consideration: positive membership, neutral membership, and negative membership degrees, thereby enabling more comprehensive representation of the complexity and ambiguity in human preferences. The proposed method integrates three main criteria through this approach: student interest measured through structured questionnaires, academic competence based on transcript analysis, and supervisor suitability based on expertise and availability. The developed PFDM has been proven to satisfy all basic metric axioms—non-negativity, identity, symmetry, and triangle inequality—with values bounded within the [0,1] interval. This paper not only provides a theoretical contribution to the development of fuzzy distance measures but also offers a practical solution for research topic recommendation.]]>
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