TY - JOUR
T1 - Law of trichotomy for triangular fuzzy numbers based on admissible orders
AU - Zumelzu, Nicolás
AU - Díaz, Roberto
AU - Mansilla, Edmundo
AU - Chalco-Cano, Yurilev
AU - Bedregal, Benjamín
N1 - Publisher Copyright:
© The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2025.
PY - 2026/4
Y1 - 2026/4
N2 - 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.
AB - 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.
KW - admissible order
KW - fuzzy numbers
KW - Law of trichotomy
KW - positive and negative fuzzy numbers
UR - https://www.scopus.com/pages/publications/105024747882
U2 - 10.1007/s40314-025-03568-2
DO - 10.1007/s40314-025-03568-2
M3 - Article
AN - SCOPUS:105024747882
SN - 2238-3603
VL - 45
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 3
M1 - 85
ER -