L型广义扩张原理及其在模糊集范畴中的应用

首先给出了L型模糊集的广义扩张原理,并讨论了它的基本性质;然后定义了两个L型模糊集范畴■(L)与■(L),并证明了范畴■(L)与范畴Set同构且范畴■(L)同构于范畴■(L)的一个子范畴.研究结果可应用于泛型信息处理设计.

模糊集范畴的性质

定义一种模糊集范畴F,讨论了F具有的范畴性质:F与子集范畴之间的关系;F上的态射用α-截集表示的条件;F上态射和映射的关系:证明了F的乘积、等子、余等子、拉回和极限等存在,并给出它们的具体形式.

模糊集范畴及集合范畴上的模

本文构造了在完备格上模糊集范畴.利用极小扩展原则和范畴的性质,获得了函子Uα构成集合范畴上的模结构,推广了P.Eklund的结论.

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.