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A Natural Fuzzy Order on Fuzzy Numbers

  • Hui Kou
  • Mingchun Xie
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Abstract

This paper introduces a natural fuzzy order on fuzzy numbers that extends the natural orders on real numbers and interval numbers. We investigate its completeness properties and show that the space of uniformly bounded fuzzy numbers is conically complete and conically cocomplete, and that it is complete if and only if the underlying continuous t-norm is the Gödel t-norm. Moreover, it is proved that this space constitutes a [0,1]-enriched domain if and only if the underlying continuous t-norm satisfies the (S) condition. These results provide a foundation for ordering fuzzy numbers.

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Cite

BibTeXRIS
BibTeX
@misc{kou2026natural,
  title = {{A Natural Fuzzy Order on Fuzzy Numbers}},
  author = {Hui Kou and Mingchun Xie},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09811},
  eprint = {2609.09811},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09811},
}
RIS
TY  - UNPB
TI  - A Natural Fuzzy Order on Fuzzy Numbers
AU  - Hui Kou
AU  - Mingchun Xie
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09811
UR  - https://arxiv.org/abs/2609.09811
AB  - This paper introduces a natural fuzzy order on fuzzy numbers that extends the natural orders on real numbers and interval numbers. We investigate its completeness properties and show that the space of uniformly bounded fuzzy numbers is conically complete and conically cocomplete, and that it is complete if and only if the underlying continuous t-norm is the Gödel t-norm. Moreover, it is proved that this space constitutes a [0,1]-enriched domain if and only if the underlying continuous t-norm satisfies the (S) condition. These results provide a foundation for ordering fuzzy numbers.
ER  -