L-预拓扑空间的局部连通性

在L-闭包空间的连通性基础上定义了L-预拓扑空间的局部连通性,并给出了局部连通的L-预拓扑空间的等价刻画,然后讨论了局部连通L-预拓扑空间的一些性质.最后证明了局部连通L-预拓扑空间与连续映射构成的范畴是一个弱拓扑范畴.

区间值模糊滤子范畴

讨论区间值模糊滤子范畴IVF和Hausdorff区间值模糊滤子范畴IVFHau中乘积、余积、等子、余等子存在性及构造。证明IVF和IVFHau都不是完备范畴而IVF是余完备范畴。也证明IVF不仅有许多弱拓扑满子范畴,也有许多非弱拓扑满子范畴。

Category of Generalized Intuitionistic Fuzzy Sets

In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.