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<p>This paper explores ordinal sums of a family of t-norms and t-conorms on bounded posets. Initially, we introduce the <i>z</i>-ordinal sum of t-norms on bounded posets, which is defined for a collection of t-norms indexed by a bounded meet semilattice. Subsequently, we define the <i>h</i>–<i>z</i>-ordinal sum of t-norms using interior operators, which extends the previously defined <i>z</i>-ordinal sum. Finally, we provide sufficient conditions under which a t-norm on a bounded meet semilattice can be expressed as an <i>h</i>–<i>z</i>-ordinal sum. For t-conorms, we present dual results. Our findings notably extend the ordinal sum introduced by Dvor̆ák and Holc̆apek (Inf Sci 515:116–131 , 2020).</p>

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On z-ordinal sums of t-(co)norms on bounded posets

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Taotao Cao,
  • Xiaochuan Liu

摘要

This paper explores ordinal sums of a family of t-norms and t-conorms on bounded posets. Initially, we introduce the z-ordinal sum of t-norms on bounded posets, which is defined for a collection of t-norms indexed by a bounded meet semilattice. Subsequently, we define the h–z-ordinal sum of t-norms using interior operators, which extends the previously defined z-ordinal sum. Finally, we provide sufficient conditions under which a t-norm on a bounded meet semilattice can be expressed as an h–z-ordinal sum. For t-conorms, we present dual results. Our findings notably extend the ordinal sum introduced by Dvor̆ák and Holc̆apek (Inf Sci 515:116–131 , 2020).