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<p>In this paper, we first introduce the concept of <i>L</i>-fuzzy rough approximation operators generated by <i>L</i>-fuzzy filters of residuated lattices. Based on this definition, some properties related to <i>L</i>-fuzzy rough approximation operators are discussed. In addition, we verify that all <i>L</i>-fuzzy filters of a residuated lattice compose an <i>L</i>-convex structure and study its basic properties. Specifically, within the framework of <i>L</i>-fuzzy approximation spaces and <i>L</i>-convex spaces, we prove that <i>L</i>-convex hull operators and <i>L</i>-fuzzy upper approximation operators are commutative.</p>

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L-fuzzy rough approximation operators and L-convex structures in residuated lattices

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Xiao-Wu Zhou,
  • Yan Yan Dong

摘要

In this paper, we first introduce the concept of L-fuzzy rough approximation operators generated by L-fuzzy filters of residuated lattices. Based on this definition, some properties related to L-fuzzy rough approximation operators are discussed. In addition, we verify that all L-fuzzy filters of a residuated lattice compose an L-convex structure and study its basic properties. Specifically, within the framework of L-fuzzy approximation spaces and L-convex spaces, we prove that L-convex hull operators and L-fuzzy upper approximation operators are commutative.