有序模糊集的Yoneda完备性与平坦完备性
Yoneda completeness and flat completeness of ordered fuzzy sets
摘要：
本文研究了Quantale上的序模糊集的Yoneda完备性和平坦完备性，这些序模糊集是通过赋予单位区间一个连续的三角范数而得到的。这两个概念都是序论中有向完备性到模糊集的自然扩张。米田完备性要求每个前向柯西网收敛（有米田极限），而平坦完备性要求每个平坦权（偏序集理想的对应物）有上确界。证明了平坦完备性蕴涵Yoneda完备性，但只有当相关的三角模同构于Lukasiewicz t-模或积t-模时，其逆蕴涵才成立.
英文摘要：
This paper studies Yoneda completeness and flat completeness of ordered fuzzy sets valued in the quantale obtained by endowing the unit interval with a continuous triangular norm. Both of these notions are natural extension of directed completeness in order theory to the fuzzy setting. Yoneda completeness requires every forward Cauchy net converges (has a Yoneda limit), while flat completeness requires every flat weight (a counterpart of ideals in partially ordered sets) has a supremum. It is proved that flat completeness implies Yoneda completeness, but, the converse implication holds only in the case that the related triangular norm is either isomorphic to the Lukasiewicz t-norm or to the product t-norm.
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