分明偏序集不能简单地当作模糊偏序集  

Crisp Posets Can Not Be Roughly Considered as Fuzzy Posets

作　　者：姚卫[1] 李尧龙[2] 吴高妮[2] 

机构地区：[1]河北科技大学理学院,石家庄050018 [2]渭南师范学院数学与信息科学学院,陕西渭南714000

出　　处：《渭南师范学院学报》2013年第6期5-8,共4页Journal of Weinan Normal University

基　　金：国家自然科学基金项目(11201112);河北省自然科学基金项目(A2010000826);河北省教育厅优秀青年基金项目(Y2012020);渭南师范学院大学生创新计划项目(12XK042)

摘　　要：一般而言,分明的数学结构借助于特征函数可以看成相应的模糊结构,如拓扑和模糊拓扑、群和模糊子群以及拟阵和模糊化拟阵等.对于偏序集和模糊偏序集,似乎也是这样的.但当考虑偏序集的具体性质,如(定向)完备性时,却发生了根本性的改变.文章通过例子说明分明的完备格借助于特征函数并不一定是模糊完备格,甚至连模糊DCPO都不是.由此说明,分明偏序集不能简单地直接当作模糊偏序集.In general, crisp mathematical structures can be considered as the corresponding fuzzy structures by means of the characteristic function, for example, topology and fuzzy topology, group and fuzzy subgroup and matroid and fuzzy matroid. It seems that the regularity also holds for poset and fuzzy posets. But when we pay attention to some concrete properties of posets and fuzzy posets, for example（directed）completeness, a fundamental change appears. In this paper, we will show by some examples that a complete lattice is not necessarily a fuzzy complete lattice, even is not a fuzzy DCPO. That is to say, crisp posets can not be roughly considered as fuzzy posets.

关 键 词：(模糊)偏序集 (模糊)DCPO (模糊)完备格 

分 类 号：O153.1[理学—数学]