发表机构
School of Mathematics, Sichuan University（四川大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出模糊数上的自然模糊序，推广实数与区间数序，证明其完备性条件及富集域性质，为模糊数排序奠定基础。
AI 中文摘要
本文引入了一种模糊数上的自然模糊序，该序推广了实数与区间数上的自然序。我们研究了其完备性性质，证明了有界一致模糊数空间是锥完备且锥余完备的，并且该空间完备当且仅当底层的连续三角范数是哥德尔三角范数。此外，还证明了该空间构成一个[0,1]-富集域当且仅当底层的连续三角范数满足(S)条件。这些结果为模糊数的排序提供了基础。
英文摘要
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.
