/ / / Alg 1

Research Article

# Application of the Variable Precision Rough Sets Model to Estimate the Outlier Probability of Each Element

## Algorithm 1

Pseudo-code of the BUILD_β_OUTLIER_REGION algorithm.
 BUILD_β_OUTLIER_REGION (U, X, R): S Pseudo-code                               Comments 1     for each 2      for each 3       S1[r][q] = {[0, 0.5)}                 Start solving Sub-problem No. 1 4       S3[r][q] = {[0, 0.5)}                 Start solving Sub-problem No. 3 5      S2[r] = {[0, 0.5)}                    Start solving Sub-problem No. 2 6     for each r ∈ R 7      Pr = CLASSIFY-ELEMENTS (U, r)         Partition induced by the equiv. relation r 8      class-max = 0                    starting the null minimum value [r] 9      for each class ∈ Pr 10    case1[r][class] = {[min(c(class, X), 1 - c(class, X)), 0.5)}     Obtain the solution for the equivalence class for Case1 11    class-max = max(class-max, c(class, X), 1 - c(class, X))  Update the null minimum value[r] 12    for each           Searching the solution for the equiv. class of case2 13     q-min = min(c(class, X), 1 - c(class, X))  Minimum error of the equiv. classes according to q with elements of the equiv. class according to i 14     for each e ∈ class                     For each class element 15      q-class = CLASSIFY-ELEMENT(U, q, e)    Obtain equiv. class to which it belongs according to q 16      q-min = min(q-min, c(q-class, X), 1– c(q-class, X))     Update the minimum value 17     case2[r][q][class] = [0, q-min)}     Obtain the solution of the equiv. class for Case 2 18     S1[r][q] = S1[r][q] ∩ (case1[r][class] ∪ case2[r][q][class])  Update S1 with new ranges of the equiv. class 19    S2[r] = S2[r] ∩ {[class-max, 0.5)}      Update S2 with new ranges of the equiv. class 20  for each                        Update S3 from the S1 values 21   for each 22    S3[q][r] = S1[r][q] ∩ S1[q][r]     Obtain the solution for which the internal border r is equal to q 23  for each               Calculate the outlier region for each internal border 24   A = {}          β for which the internal border r contains the other internal border 25   for each 26    A = A ∪ (S1[q][r]–S3[q][r]–S2[q])                    Update set A 27   S[r] = {[0, 0.5)} - A − S2[r]    Values for which the internal border r has no internal border 28  return S                              Return the solution

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