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<p>The law of trichotomy for real numbers plays an important role in real analysis. However, there are several equivalent versions of this law that, when adapted to the context of fuzzy numbers, depending of the associated order, may not be equivalent. In this work, we will consider the class of triangular fuzzy numbers (TFNs) equipped with an admissible order and investigate necessary (and sufficient in some cases) conditions that the admissible order must have to satisfy certain versions of the trichotomy law for TFNs.</p>

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Law of trichotomy for triangular fuzzy numbers based on admissible orders

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Nicolás Zumelzu,
  • Roberto Díaz,
  • Edmundo Mansilla,
  • Yurilev Chalco-Cano,
  • Benjamín Bedregal

摘要

The law of trichotomy for real numbers plays an important role in real analysis. However, there are several equivalent versions of this law that, when adapted to the context of fuzzy numbers, depending of the associated order, may not be equivalent. In this work, we will consider the class of triangular fuzzy numbers (TFNs) equipped with an admissible order and investigate necessary (and sufficient in some cases) conditions that the admissible order must have to satisfy certain versions of the trichotomy law for TFNs.