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arXiv · 1607.03212

Yoneda completeness and flat completeness of ordered fuzzy sets

Wei Li·Hongliang Lai·Dexue Zhang
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Abstract

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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Wei Li, Hongliang Lai, Dexue Zhang. 2016-07-12. Yoneda completeness and flat completeness of ordered fuzzy sets. https://doi.org/10.1016/j.fss.2016.06.009

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