Abstract: By introducing random characteristics into function inverse P-sets and improving it, the concept and structure of random function inverse P-sets (packet sets) is proposed, which is an ordered pair of cantor sets composed of random function internal inverse P-set and random function outer inverse P-set. Also, it is pointed that random function inverse P-sets is an expansion model of function inverse P-sets, while function inverse P-sets is a case of random function inverse P-sets. Based on the concepts of random function inverse P-sets, its random feature theorems and the dependent relationship theorems between random function inverse P-sets and its attributes are obtained. So the random function inverse P-sets extend the application field of function inverse P-sets.

Key words: function inverse P-sets, random function inverse P-sets, random characteristics, characteristics depending on attributes