基于拟幂等的交换单位Quantale的模糊Domain  

Fuzzy Domains based on a preidempotent unital commutative Quantale

作　　者：姚卫[1] 李颜[1] 

机构地区：[1]河北科技大学理学院,河北石家庄050018

出　　处：《河北科技大学学报》2013年第2期119-124,共6页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金资助项目(11201112);河北省自然科学基金资助项目(A2010000826);河北省教育厅优秀青年基金资助项目(Y2012020);河北省高等学校自然科学基金资助项目(Z2011139)

摘　　要：基于一个拟幂等的交换单位Quantale,用模糊集的方法重新研究了量化Domain理论,主要定义了模糊DCPO上的模糊Scott拓扑,建立了满层的L-滤子的Scott收敛理论,证明了模糊DCPO范畴的笛卡尔闭性。虽然所得结论和已有文献中的基本一样,但是证明过程却有很大不同。结果表明,拟幂等的交换单位Quantale是用模糊集方法研究量化Domain的最宽泛的格。Based on a preidempotent commutative unital Quantale,quantitative Domain theory is studied by using the approach of fuzzy sets.Fuzzy Scott topology is defined on fuzzy DCPOs,the filter-theoretical Scott converngence theory is established and the cartesian-closedness of the category of fuzzy DCPOs is proved.Although the obtained results are similar to those in the existing literatures,the proofs are very different from them.These results also indiacte that a preidempotent commutative unital Quantale is the most general lattice in studying quantitative Domain theory by fuzzy-set approach.

关 键 词：交换单位Quantale 拟幂等 模糊DCPO 模糊Scott开集 笛卡尔闭 Scott收敛 

分 类 号：O159[理学—数学] O153.1[理学—基础数学]