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<p>This article focuses on two distributive equations of <i>k</i>-generated implications over uninorms. First, we establish several necessary and sufficient conditions for these equations when <i>I</i> is a <i>k</i>-generated implication. Applying the relationships among different generated implications, we then derive the corresponding solutions for <i>f</i>-, <i>g</i>- and <i>h</i>-generated implications. These findings contribute to the theoretical understanding of distributive equations.</p>

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On two distributive equations for k- (f-, g-, h-) generated implications over uninorms

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Bing-bing Zhou,
  • Zhi-qiang Liu

摘要

This article focuses on two distributive equations of k-generated implications over uninorms. First, we establish several necessary and sufficient conditions for these equations when I is a k-generated implication. Applying the relationships among different generated implications, we then derive the corresponding solutions for f-, g- and h-generated implications. These findings contribute to the theoretical understanding of distributive equations.