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<p>Sheffer stroke which was proposed by Sheffer can be utilized as a single logical connective to constitute the classical logic system. However, the problems of data classification and decision-making often are described by natural language rather than crisp numbers in artificial intelligence (AI). The requirement of dealing with the word in AI inspires people to study the Sheffer stroke operation on a partly ordered set. Therefore, this paper mainly discusses the Sheffer stroke in a partly ordered set (for short, <i>P</i>-Sheffer stroke) and expresses other logical connectives with the <i>P</i>-Sheffer stroke which is similar to the Sheffer stroke in classical logic. Practically speaking, a <i>P</i>-Sheffer stroke defined on a partly ordered set is firstly axiomatized. And then four <i>L</i>-fuzzy negations, a t-norm and a t-conorm defined on a partly ordered set are respectively generated by the <i>P</i>-Sheffer stroke. Further, four fuzzy implications defined on a lattice are constructed with the <i>P</i>-Sheffer stroke. Finally, we study two properties of fuzzy reasoning involved in the <i>P</i>-Sheffer stroke. Moreover, the application of <i>P</i>-Sheffer stroke is shown by two examples in real-life problem.</p>

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Investigation of P-Sheffer stroke on a partly ordered set

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Dechao Li,
  • Fazhan Chen,
  • Chao Yang

摘要

Sheffer stroke which was proposed by Sheffer can be utilized as a single logical connective to constitute the classical logic system. However, the problems of data classification and decision-making often are described by natural language rather than crisp numbers in artificial intelligence (AI). The requirement of dealing with the word in AI inspires people to study the Sheffer stroke operation on a partly ordered set. Therefore, this paper mainly discusses the Sheffer stroke in a partly ordered set (for short, P-Sheffer stroke) and expresses other logical connectives with the P-Sheffer stroke which is similar to the Sheffer stroke in classical logic. Practically speaking, a P-Sheffer stroke defined on a partly ordered set is firstly axiomatized. And then four L-fuzzy negations, a t-norm and a t-conorm defined on a partly ordered set are respectively generated by the P-Sheffer stroke. Further, four fuzzy implications defined on a lattice are constructed with the P-Sheffer stroke. Finally, we study two properties of fuzzy reasoning involved in the P-Sheffer stroke. Moreover, the application of P-Sheffer stroke is shown by two examples in real-life problem.