It has four main parts as shown −
● Fuzzification Module − It transforms the system inputs, which are crisp numbers, into fuzzy sets. It splits the input signal into five steps such as −
| LP | x is Large Positive |
| MP | x is Medium Positive |
| S | x is Small |
| MN | x is Medium Negative |
| LN | x is Large Negative |
● Knowledge Base − It stores IF-THEN rules provided by experts.
● Inference Engine − It simulates the human reasoning process by making fuzzy inference on the inputs and IF-THEN rules.
● Defuzzification Module − It transforms the fuzzy set obtained by the inference engine into a crisp value.
The membership functions work on fuzzy sets of variables.
Membership Function
Membership functions allow you to quantify linguistic term and represent a fuzzy set graphically. A membership function for a fuzzy set A on the universe of discourse X is defined as µA:X → [0,1].
Here, each element of X is mapped to a value between 0 and 1. It is called membership value or degree of membership. It quantifies the degree of membership of the element in X to the fuzzy set A.
● x axis represents the universe of discourse.
● y axis represents the degrees of membership in the [0, 1] interval.
There can be multiple membership functions applicable to fuzzify a numerical value. Simple membership functions are used as use of complex functions does not add more precision in the output.
All membership functions for LP, MP, S, MN, and LN are shown as below −
The triangular membership function shapes are most common among various other membership function shapes such as trapezoidal, singleton, and Gaussian.
Here, the input to 5-level fuzzifier varies from -10 volts to +10 volts. Hence the corresponding output also changes.