Positive Macroscopic Approximation for Fast Attribute Reduction

Algorithm 2

PMA.

Inputs:

𝑈: the universe

𝑃∶𝑃={𝑎₁,𝑎₂,…,𝑎_𝑡}⊆𝐶, a condition attribute subset

𝐷∶𝐷={𝑑}, a decision attribute set

Output:

PMA𝜌_𝑡: a family of boundary regions

Begin

Sept  1. PMA𝜌_𝑡=⟨∅⟩,  𝑃₀=∅,𝜋^IT_𝑃0={𝑈} // regard the universe as a root IT-block

Step  2. For 𝑖=1 to 𝑡 do

     𝑃_𝑖=𝑃_𝑖−1∪{𝑎_𝑖}      // generate an element 𝑃_𝑖 of a positive sequence

     𝜋^IT_𝑃𝑖=𝜔^IT_𝑎𝑖(𝜋^IT_𝑃𝑖−1)       // derive IT-blocks with respect to 𝑃_𝑖 from those with respect to 𝑃_𝑖−1

     BND_𝑃𝑖𝜋_𝐷=∪{𝑋∈𝜋^IT_𝑃𝑖}    // obtain the boundary region by means of IT-blocks

     PMA𝜌_𝑡=PMA𝜌_𝑡+{BND_𝑃𝑖(𝜋_𝐷)} // add the boundary region to the sequence

Step  3. Output PMA𝜌_𝑡

End.