中文摘要：

基于函数S-粗集，结合函数迁移的随机性，提出了函数单向SPF-粗集概念，并给出它的数学结构。研究了函数单向SPF-粗集概率特性。证明了在概率的意义下，函数单向SPF-粗集是函数S-粗集，函数单向S-粗集的推广；函数S-粗集，函数单向S-粗集是函数单向S-粗集的特例。

英文摘要：

Based on function S-rough sets and the randonmess of function transfer, the concept of function one-direction SPF- rough sets was put forth, and their mathematical structure was given. The probability characteristic of function one-direction SPF- rough sets was also discussed. It was proved that a function one-direction SPF-rough set was the generalization of function one-di- rection SPF-rough sets, and the function one-direction S-rough sets was a special case of function one-direction Set-rough sets according to the probability.