Approximation operator applications in polytomous knowledge structures

Bochi Xu

doi:10.1007/s40314-025-03305-9

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Approximation operator applications in polytomous knowledge structures

2025-07-04

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Bochi Xu

李锦锦 (Jinjin Li) *

DOI：10.1007/s40314-025-03305-9

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Abstract

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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.

Keywords:

Upper (lower) rough approximation operator

Complete completely distributive lattice

Polytomous knowledge state

Polytomous knowledge structure