相对Fuzzy集、相对Fuzzy点和相关子空间

RELATIVELY FUZZY SET, RELATIVELY FUZZY POINT AND THE ASSOCIATE SUBSPACE

本文首次引进相对隶属度，相对Ｆｕｚｚｙ集、相对Ｆｕｚｚｙ点和相关子空间的概念，讨论了相对运算的基本性质；证明了相对Ｆｕｚｚｙ集族Ｉ＾ＸＡ是完全分配格，以及相关算子ｆ是从Ｉ＾Ｘ到Ｉ＾ＸＡ的满广义序同态；引进并考察了非退化相对Ｆｕｚｚｙ点，证明了非退化相对Ｆｕｚｚｙ点之集ＭＡ恰是Ｉ＾ＸＡ的所有非零Ｕ－既约元之集，从而Ｉ＾ＸＡ（ＭＡ）＝Ｉ＾ＸＡ是以ＭＡ为分子集的分子格。

In this paper,the concepts of relative grade of membership, relatively fuzzy set,relatively fuzzy point and associate subspsace are introduced, the basic properties of the relative operation are discussed;it is proved that the family of relatively fuzzy sets is a completely distributive lattice;it is proved that the associate operator of is a surjective generatived order homomorphism from I￣x to the concept of the non-degeneracy relatively fuzzy point is introduced and discussed, it is proved that the set of the non-degeneracy relatively fuzzy points just is the set of the all molecules,and then that(MA) equals is the molecular lattice in MA as the molecular set;the relation between the normal sublattice and the associate molecular lattice of the molecular lattice I￣x is discussed,it is proved that and is algebraically homomorphic;the concepts of the normal subspace and the assoiate subspace of the fuzzy cotopological space is introduced,its basic properties are discussed,it is proved that the two subspaces are topologically homeomorphic;the invariant properties of arbitrary topological molecular lattice under homeomorphisms are discued;some hereditarily properties of the fuzzy cotopological space on its normal subspace and the associate subspace are discussed.In this paper,the first section not only used as the basis of other sections,but also has the independent sense.