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<p>Overlap function <i>O</i> and grouping function <i>G</i> on the complete lattice <i>L</i> are significant logical operators for rough sets. Granular variable precision fuzzy rough set can effectively handle complex uncertain problems. Inspired by the above two facts, this paper introduces two innovative models of granular variable precision <i>L</i>-fuzzy (<i>O</i>,&#xa0;<i>G</i>)-rough sets and studies their basic properties. The first model broadens Li’s granular model from the unit interval [0,&#xa0;1] to complete lattice <i>L</i>, while maintaining all the properties of Li’s model. The second model, which can be viewed as a modification of the first, not only retains the properties of the first model but also fulfills the comparable property (lower approximation is less than upper approximation). This addresses the defects of numerous variable precision fuzzy rough sets, including Li’s granular model. On this basis, this paper further investigates the idempotent properties, definable sets, and the <i>L</i>-fuzzy topological structures induced by the second model.</p>

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Two granular variable precision L-fuzzy (O, G)-rough sets

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Jing-Wen Xie,
  • Ling-Qiang Li,
  • Dan-dan Zou

摘要

Overlap function O and grouping function G on the complete lattice L are significant logical operators for rough sets. Granular variable precision fuzzy rough set can effectively handle complex uncertain problems. Inspired by the above two facts, this paper introduces two innovative models of granular variable precision L-fuzzy (O, G)-rough sets and studies their basic properties. The first model broadens Li’s granular model from the unit interval [0, 1] to complete lattice L, while maintaining all the properties of Li’s model. The second model, which can be viewed as a modification of the first, not only retains the properties of the first model but also fulfills the comparable property (lower approximation is less than upper approximation). This addresses the defects of numerous variable precision fuzzy rough sets, including Li’s granular model. On this basis, this paper further investigates the idempotent properties, definable sets, and the L-fuzzy topological structures induced by the second model.