Positive Macroscopic Approximation for Fast Attribute Reduction

Algorithm 3

PMA-AR.

Inputs:

𝑈: the universe

𝐶∶𝐶={𝑎₁,𝑎₂,…,𝑎_𝑛}, a condition attribute set

𝐷∶𝐷={𝑑}, a decision attribute set

Output:

red: a reduct of 𝐶

Begin

Sept  1. 𝑃=∅,𝜋^IT_𝑃={𝑈},BND_𝑃𝜋_𝐷=𝑈,𝑅=𝐶

Sept  2. Compute BND_𝐶(𝜋_𝐷) by Algorithm 2

Step  3. While BND_𝑃(𝜋_𝐷)≠BND_𝐶(𝜋_𝐷) and 𝑅≠∅ do {

      𝑎_max=null,𝜋^IT_max=∅,BND_max𝜋_𝐷=∅,Sig𝑎_max,𝑃,𝐷=−1

     For 𝑖=1 to |𝑅| do {

      𝜋^IT_{𝑃∪{𝑟𝑖}}=𝜔^IT_𝑟𝑖(𝜋^IT_𝑃) // 𝑟_𝑖 denotes the No. 𝑖 attribute in 𝑅

      BND_{𝑃∪{𝑟𝑖}}𝜋_𝐷=∪{𝑋∈𝜋^IT_{𝑃∪{𝑟𝑖}}}

      Sig𝑟_𝑖,𝑃,𝐷=BND_𝑃𝜋_𝐷−BND_{𝑃∪{𝑟𝑖}}𝜋_𝐷/|𝑈|

      If Sig𝑟_𝑖,𝑃,𝐷>Sig𝑎_max,𝑃,𝐷 then {

         𝑎_max=𝑟_𝑖,𝜋^IT_max=𝜋^IT_{𝑟𝑃∪𝑖},BND_max𝜋_𝐷=BND_{𝑃∪{𝑟𝑖}}(𝜋_𝐷)

         Sig𝑎_max,𝑃,𝐷=Sig𝑟_𝑖,𝑃,𝐷

      } //end If

     }//end For

     𝑃=𝑃∪𝑎_max,𝜋^IT_𝑃=𝜋^IT_max,BND_𝑃𝜋_𝐷=BND_max𝜋_𝐷,𝑅=𝑅−{𝑎_max}

   }//end While

Step  4. Let red=𝑃