A New Method for Fracturing Wells Reservoir Evaluation in Fractured Gas Reservoir

Table 2

The major function used in fuzzy logic presented by Zoveidavianpoor et al. [6].

Function name	Parametric representation	Graphical representation
Triangular function	𝜇()=()𝑥,𝑎,𝑏,𝑐0𝑥≤𝑎𝑥−𝑎()()()𝑏−𝑎𝑥∈𝑎,𝑏𝑐−𝑥()()𝑐−𝑏𝑥∈𝑏,𝑐0𝑥≥𝑐
Trapezoidal function	𝜇()=()𝑥,𝑎,𝑏,𝑐,𝑑0𝑥<𝑎,𝑥>𝑑𝑥−𝑎()()𝑏−𝑎𝑎≤𝑥≤𝑏𝑑−𝑥(𝑑−𝑐)𝑐≤𝑥≤𝑑1𝑏<𝑥<𝑐
Normalized Gaussian function	𝜇𝑥,𝜎𝑖,𝑐𝑖=exp^(𝑥−𝑐𝑖)2/2𝜎2𝑖
Two sigmoidal functions	𝜇𝑥,𝛼1,𝜉1,𝛼2,𝜉2=1+𝑒^−𝛼1(𝑥−𝜉1)−1−1+𝑒^−𝛼2(𝑥−𝜉2)−1
Generalized bell function	𝜇𝑥,𝛼𝑖,𝛽,𝜉=1+𝑥−𝜉𝛼^2𝛽−1