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<p>In the past, many scholars studied the construction of different binary operators on different intervals, which indicates that studying the construction of different binary operators on different intervals is a hot field. Moreover, no scholars have studied the construction of semi-overlap (grouping) functions on complete lattices before. First, based on the concept of semi-overlap functions on unit closed intervals proposed by (Zhang et&#xa0;al. <CitationRef CitationID="CR59">2022</CitationRef>), this paper provides the definitions of semi-overlap (grouping) functions on complete lattices, respectively. And then, two new type of semi-overlap (grouping) functions on a complete lattice is constructed, and illustrates them with some examples. In addition, some related properties of semi-overlap (grouping) functions on complete lattices, such as the (cross-)migrativity and homogeneity are also introduced, respectively.</p>

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Two novel construction methods of semi-overlap (grouping) functions on complete lattices

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Kuanyun Zhu,
  • Yuqiong Luo,
  • Jingru Wang

摘要

In the past, many scholars studied the construction of different binary operators on different intervals, which indicates that studying the construction of different binary operators on different intervals is a hot field. Moreover, no scholars have studied the construction of semi-overlap (grouping) functions on complete lattices before. First, based on the concept of semi-overlap functions on unit closed intervals proposed by (Zhang et al. 2022), this paper provides the definitions of semi-overlap (grouping) functions on complete lattices, respectively. And then, two new type of semi-overlap (grouping) functions on a complete lattice is constructed, and illustrates them with some examples. In addition, some related properties of semi-overlap (grouping) functions on complete lattices, such as the (cross-)migrativity and homogeneity are also introduced, respectively.