Neuro-fuzzy systems are those fuzzy systems which are based on Artificial Neural Network (ANN) theory in order to determine their properties by processing data samples. It harnesses the abilities of both fuzzy logic and ANNs. The mathematical properties of ANNs are required for tuning rule based fuzzy systems which approximate the human’s way of processing information. Adaptive Neuro-Fuzzy inference system (ANFIS) is a specific approach of Neuro-Fuzzy methodology. ANFIS shows significant results in modelling of nonlinear functions. The data sets describing system behaviour provides parameters for membership function. Learning in ANFIS is done by adjusting system parameters according to a given error criterion. The ANFIS model has higher accuracy rates than that of self-contained neural network model.
Fuzzy sets and fuzzy sets operations are the subjects and verbs of fuzzy logic. If-Then rule statements are used to formulate the conditional statements that comprise fuzzy logic. Fuzzy if-then rules or fuzzy conditional statements are expressions of the form IF A THEN B, where A and B are labels of fuzzy sets characterized by appropriate membership functions. Fuzzy Rules can be categorized into two types:
1) Fuzzy Mapping Rules- It describes a functional mapping relationship between inputs and an output using linguistic terms.
2) Fuzzy Implication Rules- It describes a generalized logic implication relationship between two logic formula involving linguistic variable and imprecise linguistic terms.
The Artificial Neural Network (ANN) can be viewed as weighted directed graphs in which artificial neurons are nodes and directed edges are connections between neurons. It is an information processing system, which analyses data by passing it through several simulated processors. By designing training algorithms we can adjust the weights of ANN in order to obtain the desired output from the network. The backpropagation algorithm is used in layered feed-forward ANNs. Artificial neurons send their signals “forward”, and the errors are propagated backwards. The network receives inputs by neurons in the input layer, and the output of the network is given by the neurons on an output layer. Then the difference between actual and expected results is calculated. There may be one or more intermediate hidden layers. The idea of the backpropagation algorithm is to reduce this difference, until the ANN learns the training data. The backpropagation algorithm uses supervised learning and the training begins with random weights. Since the time for training the network grows exponentially therefore for practical reasons ANNs implementing the backpropagation algorithm do not have too many layers.
Fig Standard three-layer feed-forward network architecture
Anupriya Asthana, ECE Dept