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中文摘要：
引入群范畴上格值结构、层结构、L-fuzzy结构提升范畴概念,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;层结构是把群上局部信息合理粘连成整体信息的数学结构;而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—Frankel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,建立格值结构、层结构、L-fuzzy结构这三种不同数学结构之间的联系,证明在范畴层面上述三种结构是同构的。
英文摘要：
The concepts of lifting category of sheaf structures, latticed-valued structures, L-fuzzy structures based on the category of groups are introduced. In mathematics, lattice-valued structures are a kind of categorical structures, which catches the pointless characterization of many evaluations in mathematics about uncertainty. Sheaves are another kind of categorical structures, which can combine the local information into global information in a space. But 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. We give the connections among lattice-valued structures, sheaf structures and L-fuzzy structures by proving that the categories of these three different structures are isomorphic.
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