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<p>This study proposes an innovative integration of knowledge space theory with rough set theory, developing a framework for generating polytomous knowledge structures through approximation operators. In contrast to traditional rough set methodologies that primarily analyze properties of upper or lower approximations for a set, our work specifically concentrates on constructing polytomous knowledge structures by upper or lower rough approximation operators defined within a complete completely distributive lattice structure. The proposed methodology provides a novel perspective on rough set through knowledge space theory. Some topological properties of polytomous knowledge structures generated through approximation operators are also discussed. And using rough set methods, the proof of some theorems and propositions about the polytomous knowledge structures are investigated.</p>

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Approximation operator applications in polytomous knowledge structures

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Bochi Xu,
  • Jinjin Li

摘要

This study proposes an innovative integration of knowledge space theory with rough set theory, developing a framework for generating polytomous knowledge structures through approximation operators. In contrast to traditional rough set methodologies that primarily analyze properties of upper or lower approximations for a set, our work specifically concentrates on constructing polytomous knowledge structures by upper or lower rough approximation operators defined within a complete completely distributive lattice structure. The proposed methodology provides a novel perspective on rough set through knowledge space theory. Some topological properties of polytomous knowledge structures generated through approximation operators are also discussed. And using rough set methods, the proof of some theorems and propositions about the polytomous knowledge structures are investigated.