L-fuzzy集理论的范畴基础与层表示

摘要
鉴于L-fuzzy集在理论上的重要性和应用上的广泛性,旨在建立L-fuzzy集理论的范畴基础与它的层表示,提出完备范畴中对象上的格值结构概念,这一概念是L-fuzzy结构在范畴层面上的提升,进一步提出完备范畴上格值结构提升范畴概念,证明了在集合范畴中L-fuzzy结构与格值结构是同构的.以集层、群层、环层和左R-模层以及Grothendieck层等概念为基础,提出完备范畴中对象上的层结构以及完备范畴上层结构提升范畴概念,证明了在集合范畴中L-fuzzy结构与层结构也是同构的.
作者
汤建钢罗懋康汤娟 TANG Jian-Gang LUO Mao-Kang TANG Juan
作者单位
伊犁师范学院数学与统计学院,伊宁,835000/四川大学数学学院,四川成都,610064/四川大学电子信息学院,四川成都,610064
刊期
2013年8期 ISTIC PKU
关键词
L-fuzzy结构格值结构层结构提升范畴同构关系 L-fuzzy structure lattice-valued structure sheaf structure lifting category isomorphic relation sheaves representation

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