基于群范畴的L-fuzzy结构提升范畴及其表示  

The Lifting Category of L-fuzzy Structures Based on the Category of Groups and Its Representation

作　　者：桂跃宇 汤建钢[2] 

机构地区：[1]伊犁职业技术学院基础部,新疆伊宁835000 [2]伊犁师范学院数学与统计学院,新疆伊宁835000

出　　处：《模糊系统与数学》2012年第5期87-93,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11161050)

摘　　要：引入群范畴上L-fuzzy结构提升范畴与格值结构提升范畴概念,L-fuzz结构是在逻辑层面表达群理论多值语义的有点化描述,也是Zermelo—Fra。nkel公理集合理论和各种代数形式理论的格值模型的语义赋值,而格值结构是在范畴层面表达群理论多值语义的无点化描述,本文建立了L-fuzzy结构与格值结构这两种不同数学结构之间的联系,证明了在范畴层面上述两种结构是同构的。给出了基于群范畴的L-fuzzy结构的格值结构表示。The concepts of the lifting category of L-fuzzy structures and the lifting category of latticed- valued structures based on the category of groups are introduced. In mathematics, L-fuzzy structures are a pointwise characterization of kinds of evaluations in mathematics about uncertainty, and are a kind of evaluation of semantic of lattice-valued models of Zermelo-Fraenkel axiomatic set theory and kinds of formal algebraic theory, lattice-valued structures are a kind of categorical structures, which catches the pointless characterization of many evaluations in mathematics about uncertainty. We give the connections among L-fuzzy structures and lattice-valued structures by proving that the categories of these two different structures are isomorphic.

关 键 词：群范畴 L-fuzzy结构 格值结构 提升范畴 同构关系 

分 类 号：O159[理学—数学]