FBFN_OLS

FBFN_OLS - KartavyaNeema NeuroFuzzySystem...

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Kartavya Neema
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Neuro Fuzzy System
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Fuzzy Basis Function Network (FBFN)
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FBFN (contd.) y Fuzzy basis function is defined by: y In FBFN, a fuzzy system is represented as a series expansion of fuzzy basis functions (FBFs). Each FBF corresponds to one fuzzy logic rule.
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Initial FBF Determination y Fuzzy based function: y Where p is: y Membership function is: y I chose 4 fuzzy rules (M). Thus, 4 membership for each input y We choose a = 1. σ = range of input/ no. of fuzzy rules. X (center) to be the input points in the given input output pair.
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FBF as Linear regression y In order to train the network, FBF is treated as a special case of linear regression y Where d(t) is the system output, e(t) is the error
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FBF as Linear regression y In order to use OLS, Matrix form is given: y Now, can we take the data and start the training to determine weights ( θ )
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y An orthogonal least squares (OLS) learning algorithm is utilized to determine the significant FBFs [i.e. Fuzzy
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FBFN_OLS - KartavyaNeema NeuroFuzzySystem...

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