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<p>This study aims to characterize the “previous” and “next” sets of <i>L</i>-fuzzy sets within certain families by employing <i>L</i>-fuzzy rough approximation operators. We generalize master fringes –critical for learning path recommendation in knowledge space theory–from dichotomous to polytomous knowledge structures, and define bottom and top spaces of equivalence classes. Propositions characterizing the master-fringe of <i>L</i>-fuzzy sets are established, including special cases under floor-inclusive and roof-inclusive conditions. Finally, a knowledge space theory application and a real-world example of personalized learning are presented.</p>

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Characterizing master fringes in L-fuzzy rough sets theory

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Bochi Xu,
  • Jinjin Li

摘要

This study aims to characterize the “previous” and “next” sets of L-fuzzy sets within certain families by employing L-fuzzy rough approximation operators. We generalize master fringes –critical for learning path recommendation in knowledge space theory–from dichotomous to polytomous knowledge structures, and define bottom and top spaces of equivalence classes. Propositions characterizing the master-fringe of L-fuzzy sets are established, including special cases under floor-inclusive and roof-inclusive conditions. Finally, a knowledge space theory application and a real-world example of personalized learning are presented.