For a general subset system Z,the concept of Z-minimal sets is defined,some characteristics of Z-continuous posets are discussed,the equivalent characterizations between the mapping preserving the Z-minimal sets and the mapping preserving _Z and the Z-supremum of Z-continuous posets are given,so the corresponding extension theorem is made.

In this paper, We define Quas Z-minimal Sets, the equivalent characterization of the Quasi Z-minimal Sets is introduced, and the mapping preserving Quasi Z-minimal Sets is given, so the two corresponding extention theorems are made by Rudin lemma.

By means of the methodology of rough set,different attribute classification methods for decision systems are first analyzed in this paper,and the attribute significance as well as the extremely small subset of the attribute relative reduction caused by a classification variety is discussed.

The authors introduce two new concepts of L - nested sets which are based on the concepts of minimal set and maximal set where L is a completely distributive lattice.

In F lattice,sixteen cut sets of l fuzzy set and corresponding decomposition theorems have been given by the use of maximal set and minimal set.

The attractor M which attracts any bounded set the following facts are proved:i) every motion on M is almost periodic;ii) for a∈M, γ(a) =ω(a) is a minimal set.

In this paper,an improved genetic algorithm (called MGA) is used to compute minimal hitting sets.

Furthermore, the computing procedure is formalized by combining SE-tree with closed nodes to generate all the minimal hitting sets.