Fuzzy systems

Module overview. The idea of a fuzzy system is introduced in this module. Its main components are described and discussed in detail using examples. The results from the fuzzification module drives the rule base. The fuzzy inference machine is developed which solves the reasoning. The methods to transform the fuzzy results of the reasoning process to crisp data is shown in detail. The mainstream in the fuzzy system of this module is the Mamdani approach which needs the defuzzification step, but the Takagi-Sugeno-type of fuzzy system is also introduced which avoids defuzzification.

Module objectives. When you have completed this module you should be able to:

1. Design a fuzzy system.
2. Fuzzify input information.
3. Describe a fuzzy inference machine using fuzzy sets.
4. Defuzzify results from the reasoning process.

Module prerequisites. Fuzzy sets.

In the previous section, elementary fuzzy terms and fuzzy logic operations have been introduced. In this section, the application to the treatment of rule-based knowledge follows. For this a rule-based fuzzy system is needed, containing a rule base and a reasoning algorithm, which is used to process crisp or fuzzy input values to a crisp or fuzzy output value , see Figure 16.1.

Figure 16.1: Rule-based fuzzy system with inputs and one output

Using multiple inputs and one output implies no restriction as a multi-input-multi-output fuzzy system can always be decomposed into multiple systems according to Figure 16.1. Such systems are the basis for the realisation of fuzzy controllers. As there are mostly crisp input values from measurements and for controllers only a crisp output , a fuzzy system must contain additional components, fuzzification and defuzzification.