PART 9Fuzzy Systems

1. Fuzzy controllers2. Fuzzy systems and NNs3. Fuzzy neural networks4. Fuzzy Automata5. Fuzzy dynamic systems

FUZZY SETS AND

FUZZY LOGICTheory and Applications

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Fuzzy Controllers

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Fuzzy Controllers

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Fuzzy Controllers

Five steps of design:

Step 1: Select linguistic states for I/O variables

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Fuzzy Controllers

Step 2: Define fuzzification functions for input variables

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Fuzzy Controllers

Step 3: Formulate fuzzy inference rules

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Fuzzy Controllers

Step 4: Making inferences by inference engine

Step 5: Define a suitable defuzzification method

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Fuzzy Controllers

Center of area method

For the discrete case:

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Fuzzy Controllers

Center of maxima method

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Fuzzy Controllers

Mean of maxima method

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Fuzzy Controllers

Mean of maxima method

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Fuzzy Controllers

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Fuzzy Controllers

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Fuzzy Controllers

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Fuzzy Controllers

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Fuzzy Controllers

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Fuzzy Controllers

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Fuzzy systems and NNs

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Fuzzy neural networks

1.Inputs, outputs of different layers, and weights are fuzzy numbers

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Fuzzy neural networks

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4. Stopping criteria

5. Fuzzy the BP algorithm

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Fuzzy automata

• Definition A fuzzy automaton its states are characterized

by fuzzy sets, and the production of responses and next states is facilitated by appropriate fuzzy relations.

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Fuzzy automata

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Fuzzy automata

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Fuzzy automata

Example : A fuzzy automaton with

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Fuzzy automata

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internal states at any time t be defined by the vectors

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Fuzzy automata

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Fuzzy automata

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Fuzzy dynamic systems

• General dynamic system

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Fuzzy dynamic systems

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Exercises

• 9.2

• 9.4