UPM Facultad de Informática Departamento de Matemática Aplicada eMathTeacher: Mamdani's Fuzzy Inference Method
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Motivation
Classical approach
Fuzzy approach

Membership functions

Fuzzy operators

FIS Introduction

Mamdani's Method
1: Evaluate antecedent
2: Obtain conclusion
3: Aggregate conclusions
4: Defuzzify
5: Summary/Conclusions

Example 1: Traffic

Example 2: Heating

Practice: FIS Creation

 

Example 1: Traffic controller

An example of a fuzzy system is a traffic controller embedded in the traffic lights of an intersection, whose purpose is to minimize the waiting time of a line of cars in a red light, as well as the length of such line. This controller is defined as follows:

Input variables

  • Arrival: Rate of car arrivals in a green light, with possible values: Very few, Few, Many and A lot. We will use the discrete range [0,30].
  • Line: Length of the line of cars in a red light, with possible values: Very Short, Short, Medium and Long. We will use the discrete range [0,30].

Output variable

  • TimeG: Time (in seconds) of the traffic light's green phase, with possible values: Short, Medium and Long. We will use the discrete range [5,50].

Membership functions: in this example we will be able to choose from triangular functions or trapezoidal functions for each variable.

Rule Base: rules will be specified throughout the exercise.

Next, we will apply Mamdani's method to this example, step by step, with a series of Java applets.

Next: Step 1