A Novel Approach of Rough Conditional Entropy-Based Attribute Selection for Incomplete Decision System

Algorithm 2

Depth-first.

Input: An incomplete decision system (𝑈,𝐶∪{𝑑}).

Output: A selected attribute subset 𝑅.

  (1) Initialize SelectAttr=Ø, unSelectAttr=𝐶

  (2) For every attribute 𝑎_𝑖∈unSelectAttr, SelectAttr=SelectAttr∪𝑎_𝑖,

     calculate the tolerance class of object 𝑢_𝑖, 𝑇_Attr𝑢_𝑖

  (3)   Calculate the conditional entropy EN(𝑑∣SelectAttr)=EN𝑑∣SelectAttr∪𝑎_𝑖

  (4)   Choose the attribute 𝑎 which minimizes EN(𝑑∣SelectAttr∪{𝑎}), that is

     choose the attribute with the maximum significance measure SIG(𝑎,SelectAttr,𝑑)

  (5)    SelectAttr=SelectAttr∪{𝑎}, unSelectAttr=unSelectAttr−{𝑎}

  (6)   If EN(𝑑∣SelectAttr)≠EN(𝑑∣𝐶), go to Step  2, otherwise 𝑅=SelecAttr

  (7) End