Fuzzy Neurons
Introduction:-The neural network models presented so far use variants of McCulloch and Pitt's neuron to build anetwork. New types of neurons have been introduced which use fuzzy membership functions asactivation functions or as functions attached to their connections. One of them is the so-called fuzzyneuron.
A fuzzy neuron has the following features, which distinguish it from the ordinary types of neurons:-
- The inputs to the neuron x_{1}, x_{2}, . . .,x_{n}represent fuzzy labels of the fuzzy input variables.
- The weights wi are replaced by functions μi which are the membership functions of the fuzzy labels x_{i}(i = 1, 2, . . .,n).
Excitatory connections are represented by MIN operation and inhibitory connections by fuzzy logic complements followed by MIN operation.
· A threshold level is not assigned. In the fuzzy neuron there is no learning. The membership functions attached to the synaptic connections do not change. The fuzzy neuron has been successfully used for handwritten character recognition.
The Neo-fuzzy neuron is a further development of the fuzzy neuron.
The features of the neo-fuzzy neuron are:
- The inputs x_{1}, x_{2}. . . x_{n}represent fuzzy variables.
- Each fuzzy segment x_{ij}attached to each of the fuzzy variables x_{i, i}= 1, m; j = 1,nare represented as connections between the input i and the output.
- In addition to the membership function μ_{ij}, which is bound to the input segment x_{ij},weights w_{ij}are also assigned, subject to a training procedure.
- The segments x_{i1}, x_{i2}, . . .,x_{il}have standard triangular membership functions; thus an input activates only two membership functions simultaneously; the sum of the degree to which an input value x'I belongs to any two neighboring membership functions μ_{ik}(x'i) and μ_{i,k 1}(x'i) is always equal to 1. Thus the COG defuzzification does not use a division and the output of the neuron can be represented by the following simple equation:
There are some training algorithms applicable to the neo-fuzzy neuron. One of them is called incremental updating (stepwise training).
Fuzzy neurons have been applied to prediction and classification problems.