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Table 1 Membership functions for six grades

From: Application of fuzzy evaluation technique and grey clustering method for water quality assessment of the coastal and estuaries of selected rivers in Sarawak

P Expression of membership function Scope
  1 (Ci ≤ CI)
PI (Ci) (CII–Ci)/(CII–CI) (I < Ci < CII)
  0 (Ci ≥ CII)
  0 (Ci ≤ CII or Ci ≥ CIII)
PII (Ci) (Ci–CI)/(CII–CI) (CI < Ci ≤ CII)
  (CII–Ci)/(CIII–CII) (CII < Ci ≤ CII)
  0 (Ci ≤ CII or Ci ≥ CII)
PIII (Ci) (Ci–CII)/(CIII–CII) (CII < Ci ≤ CIII)
  (CIV–Ci)/(CIV–CIII) (CIII < Ci ≤ CIV)
  0 (Ci ≤ CIV or Ci ≥ CV)
PIV (Ci) (Ci–CIII)/(CIV–CIII) (CIII < Ci < CIV)
  (CV–Ci)/(CV–CIV) (CIV < CV ≤ CV)
  0 (Ci ≤ CV or Ci ≥ CVI)
PV (Ci) (Ci–CIV)/(CV–CIV) (CIV < Ci ≤ CV)
  (CVI–Ci)/(CVI–CV) (CV < Ci ≤ CVI)
  0 (Ci ≤ CV)
PVI (Ci) (Ci–CV)/(CVI–CV) (CV–Ci ≤ CVI)
  1 (Ci ≥ CVI)