Example Fuzzy Expert Systems

1
Example Fuzzy Expert Systems

• Controlling water level using
• a set of rules
• more than one fuzzy value
• fuzzy associative memory

Large reservoir
Limited interval Random Constrictor
Float
Water level sensor
Valve
Motor
? L
integrator
Fuzzy Controller
L
2
Data

• input
• absolute level
• plant engineer low - OK - high
• system parameter neg - zeroish - pos
• rate of change of level
• plant engineer negative - low - high
• system parameter neg - zeroish - pos
• output
• valve opening
• plant engineer closed - slight - mid - on - full
• system parameter NL - NS - ZE - PS - PL

3
Rule base

• elicited from plant engineer
• IF Level is N AND ?Level is N THEN ValveOpen
  is NL
• N ZE NS N P NS
• ZE N NS
• ZE ZE ZE
• ZE P PS
• P N PS
• P ZE PS
• P P PL
• Fuzzy Associative Memory (FAM) matrix

?level
N
ZE
P
NL
NS
NS
N
NS
ZE
PS
ZE
level
PS
PS
PL
P
4
Membership Functions

• Level and ?Level
• ValveOpening

Negative
Positive
Zeroish
1
likelihood
OK
High
Low
Level
0 Mtrs
2 Mtrs
-2 Mtrs
Constant
Rising fast
Receding fast
?Level
0 Mtr/min
2 Mtr/min
-2 Mtr/min
NL
NS
ZE
PS
PL
1
likelihood
0
45
90
5
Fuzzy combination

• max-min combination
• e.g. Level 0.8
• ?Level -0.7
• i.e.
• FN(0.8) 0
• FZE(0.8) 0.7
• FP(0.8) 0.2
• AND
• FN(-0.7) 0.13
• FZE(-0.7) 0.8

1
0.8
0.7
likelihood
N
ZE
P
0.2
0.13
0
-2
2
0.8
-0.7
6
Fuzzy combination cont.

• the Min operation
• w1 minFZE(0.8), FN(-0.7)
• min0.7, 0.13
• 0.13
• w2 minFZE(0.8), FZE(-0.7)
• min0.7, 0.8
• 0.7
• w3 minFP(0.8), FN(-0.7)
• min0.2, 0.13
• 0.13
• w4 minFP(0.8), FZE(-0.7)
• min0.2, 0.8
• 0.2

7
Defuzzification

• from rules
• IF Level is ZE AND ?Level is ZE THEN
  ValveOpen is ZE
• ? 0.7 ZE(ValveOpen)
• using a fuzzy output to ValveOpen function
• ValveOpen 48.6 degrees

90
72
54
48.6
36
18
NL
NS
ZE
PS
PL