where\(X=\left[x_{1},\ldots,x_{n}\right]^{T}\in\mathcal{R}^{n}\)and \(y\in\mathcal{R}\) are the input and output of the fuzzy system,
respectively. \(A_{i}^{l}\ \left(i=1,2,\ldots\right)\) is the fuzzy
set of the input \(x_{i}\ (i=1,2,\ldots,n)\) and \(B^{l}\)(\(l=1,2,\ldots,N\)) is the fuzzy set of the output. The output of the
fuuzy system by considering a singleton fuzzification and the minimum
inference engine (based on the Mamdani approach) is as follows: