外P-模糊集的截集与扩展粗集模型

P-模糊集是由内、外P-模糊集构成的集合对,内、外P-模糊集是两类不同的动态模糊集。截集方法是研究模糊集理论最常用的方法,提出外P-模糊集的λ-截集、λ-强截集、区间截集及其截集粒度的概念,讨论了外P-模糊集的截集序列粒度定理、区间截集序列粒度定理,给出外P-模糊集区间截集分解定理。利用外P-模糊集粗隶属度函数的概念,给出外P-模糊集A^F的(α_F,β_F)粗集、(1_F,0_F)粗集、(α_F,β_F)概率粗集、(α_F,β_F)的变精度粗集四种粗集扩展模型,讨论了外P-模糊集的(α_F,β_F)粗集定理,并给出其数量特征及关系讨论。

Cut sets of outer P-fuzzy sets and extended rough sets models

The P-fuzzy sets are a pair of inner and outer P-fuzzy sets. Inner and outer P-fuzzy sets are two different kinds of dynamic fuzzy sets. The cut sets method is frequently used in fuzzy sets discussed. The concepts of λ-cut sets, strong λ-cut sets, interval cut sets and cut sets granularity are proposed, and the cut sets and interval cut sets granularity theorems of outer P-fuzzy sets are discussed. Then, the interval cut sets decomposition theorems of outer P-fuzzy sets are given. By using the concept of the outer P-fuzzy rough membership function, four rough sets extended models are proposed such as (α_F,β_F) rough sets, (1_F,0_F) rough sets, (α_F,β_F)probability rough sets and (α_F,β_F) variable precision rough sets. The (α_F,β_F)rough sets theorems of the outer P-fuzzy sets are discussed. In the end, the quantitative characteristics and relationship theorem are given.