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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)