相对隶属度、相对Fuzzy集和相关子空间及其性质

Relative grade of membership, relative fuzzy set and associate subspace

建立了相对隶属度、相对Ｆｕｚｚｙ集、相对Ｆｕｚｚｙ点和相关子空间等概念，研究其基本性质，证明了相对Ｆｕｚｚｙ集族ＢＡＩＸ是完全分配格，相关算子ｆ是从ＩＸ到ＢＡＩＸ的满ＧＯＨ，非退化相对Ｆｕｚｚｙ点集ＢＡＭ是ＢＡＩＸ中所有非零∪－既约元之集．得到了子分子格ＢＡＩＸ＊与相关分子格ＢＡＩ＊是代数同构的。

The concepts of relative grade of membership, relative fuzzy set, relative fuzzy point and associated subspace are introduced, their basic properties are discussed. It is proved that the family B AI X is a completely distributive lattice, the associated operator f is a surjective GOH from I X to B AI X , the set of the non degeneracy relative fuzzy is just the set of all molecules in B AI X , B AI X and B AI X * are algebraically isomorphic, generalized subspace B AI X * and associated subspace are topologically homeomorphic.