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<p>This article first defines an (<i>f</i>,&#xa0;<i>k</i>)-implication that generalizes a <i>k</i>-generated implication. It then explores the relationships of the (<i>f</i>,&#xa0;<i>k</i>)-implication to some well-known classes of fuzzy implications. It finally investigates the validity of <i>T</i>-conditionality, the law of importation and the distributivity over t-norms and t-conorms for the (<i>f</i>,&#xa0;<i>k</i>)-implications, respectively.</p>

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Generalizations of k-generated implications

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Jing Jing Yue,
  • Xue-ping Wang

摘要

This article first defines an (f, k)-implication that generalizes a k-generated implication. It then explores the relationships of the (f, k)-implication to some well-known classes of fuzzy implications. It finally investigates the validity of T-conditionality, the law of importation and the distributivity over t-norms and t-conorms for the (f, k)-implications, respectively.