(L,M)-fuzzy闭包系统与(L,M)-fuzzy闭包算子

(L,M)-fuzzy Closure System and (L,M)-fuzzy Closure Operator

定义了(L,M)-fuzzy闭包系统与(L,M)-fuzzy闭包算子的概念,建立了给定集合X上(L,M)-fuzzy闭包系统的全体FCS(L,M,X)和(L,M)-fuzzy闭包算子的全体FCO(L,M,X)之间的一一对应(在此基础上证明了(L,M)-fuzzy闭包系统空间范畴LMFCSS与(L,M)-fuzzy闭包算子空间范畴LMFCOS是同构的)。此外还证明了(2,M)-fuzzy闭包系统空间范畴2MFCSS可嵌入到(L,M)-fuzzy闭包系统空间范畴LMFCSS,(2,M)-fuzzy闭包算子空间范畴2MFCOS可嵌入到(L,M)-fuzzy闭包算子空间范畴LMFCOS。

In this paper,we studied（L,M）-fuzzy clousure system and （L,M）-fuzzy closure operator,established a one-to-one correspondence within them;cosequently,we proved that the category of（L,M）-fuzzy clousure system space andthe category of（L,M）-fuzzy clousure operator space are isomorphic.Furthermore,we studied the relationship between categories of （2,M）-fuzzy clousure system（operator） space and（L,M）-fuzzy clousure system （operator） space,proved thatthe category of（2,M）-fuzzy clousure system space can be embedded into the category of（L,M）-fuzzy clousure system spaceand the category of（2,M）-fuzzy clousure operator space can be embedded into the category of （L,M）-fuzzy clousure operator space.