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
2.
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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