Table 1: 𝛼 -level interval of coefficient parameters.

Br 𝜇 𝐿 𝑀 ( 𝑥 ) Br 𝜇 𝑅 𝑀 ( 𝑥 ) ( 𝑀 𝛼 𝑀 ) = [ 𝐿 𝛼 , 𝑀 𝑅 𝛼 ]

L: 1 ( 𝑀 2 𝑥 ) / ( 𝑀 2 𝑀 1 ) L: 1 ( 𝑥 𝑀 2 ) / ( 𝑀 3 𝑀 2 ) [ 𝑀 1 + 𝛼 ( 𝑀 2 𝑀 1 ) , 𝑀 3 𝛼 ( 𝑀 3 𝑀 2 ) ]
L: 1 ( 𝑀 2 𝑥 ) / ( 𝑀 2 𝑀 1 ) P: 1 ( ( 𝑥 𝑀 2 ) / ( 𝑀 3 𝑀 2 ) ) 2 [ 𝑀 1 + 𝛼 ( 𝑀 2 𝑀 1 ) , 𝑀 2 + 1 𝛼 ( 𝑀 3 𝑀 2 ) ]
L: 1 ( 𝑀 2 𝑥 ) / ( 𝑀 2 𝑀 1 ) E: 𝛼 2 ( 1 𝑒 𝛽 2 ( ( 𝑀 3 𝑥 ) / ( 𝑀 3 𝑀 2 ) ) ) [ 𝑀 1 + 𝛼 ( 𝑀 2 𝑀 1 ) , 𝑀 3 + ( ( 𝑀 3 𝑀 2 ) / 𝛽 2 ) l o g ( 1 𝛼 / 𝛼 2 ) ]
P: 1 ( ( 𝑀 2 𝑥 ) / ( 𝑀 2 𝑀 1 ) ) 2 L: 1 ( 𝑥 𝑀 2 ) / ( 𝑀 3 𝑀 2 ) [ 𝑀 2 1 𝛼 ( 𝑀 2 𝑀 1 ) , 𝑀 3 𝛼 ( 𝑀 3 𝑀 2 ) ]
P: 1 ( ( 𝑀 2 𝑥 ) / ( 𝑀 2 𝑀 1 ) ) 2 P: 1 ( ( 𝑥 𝑀 2 ) / ( 𝑀 3 𝑀 2 ) ) 2 [ 𝑀 2 1 𝛼 ( 𝑀 2 𝑀 1 ) , 𝑀 2 + 1 𝛼 ( 𝑀 3 𝑀 2 ) ]
P: 1 ( ( 𝑀 2 𝑥 ) / ( 𝑀 2 𝑀 1 ) ) 2 E: 𝛼 2 ( 1 𝑒 𝛽 2 ( ( 𝑀 3 𝑥 ) / ( 𝑀 3 𝑀 2 ) ) ) [ 𝑀 2 1 𝛼 ( 𝑀 2 𝑀 1 ) , 𝑀 3 + ( ( 𝑀 3 𝑀 2 ) / 𝛽 2 ) l o g ( 1 𝛼 / 𝛼 2 ) ]
E: 𝛼 1 ( 1 𝑒 𝛽 1 ( ( 𝑥 𝑀 1 ) / ( ( 𝑀 2 𝑀 1 ) ) ) L: 1 ( 𝑥 𝑀 2 ) / ( 𝑀 3 𝑀 2 ) [ 𝑀 1 ( ( 𝑀 2 𝑀 1 ) / 𝛽 1 ) l o g ( 1 𝛼 / 𝛼 1 ) , 𝑀 3 𝛼 ( 𝑀 3 𝑀 2 ) ]
E: 𝛼 1 ( 1 𝑒 𝛽 1 ( ( 𝑥 𝑀 1 ) / ( 𝑀 2 𝑀 1 ) ) ) P: 1 ( ( 𝑥 𝑀 2 ) / ( 𝑀 3 𝑀 2 ) ) 2 [ 𝑀 1 ( ( 𝑀 2 𝑀 1 ) / 𝛽 1 ) l o g ( 1 𝛼 / 𝛼 1 ) , 𝑀 2 + 1 𝛼 ( 𝑀 3 𝑀 2 ) ]
E: 𝛼 1 ( 1 𝑒 𝛽 1 ( ( 𝑥 𝑀 1 ) / ( 𝑀 2 𝑀 1 ) ) ) E: 𝛼 2 ( 1 𝑒 𝛽 2 ( ( 𝑀 3 𝑥 ) / ( 𝑀 3 𝑀 2 ) ) ) [ 𝑀 1 ( ( 𝑀 2 𝑀 1 ) / 𝛽 1 ) l o g ( 1 𝛼 / 𝛼 1 ) , 𝑀 3 + ( ( 𝑀 3 𝑀 2 ) / 𝛽 2 ) l o g ( 1 𝛼 / 𝛼 2 ) ]

L, P, and E stand for linear, parabolic, and exponential membership functions, respectively, 𝛼 1 , 𝛼 2 > 1 ; 𝛽 1 , 𝛽 2 > 0 ; 0 < 𝛼 < 1 .