1. Building a Fuzzy Expert System
Chapter 13 (Continued)
Building a Fuzzy Expert System
Air conditioner
Determining number of spare in a service center

2. Steps of Building an Expert System
Specify the problem and define linguistic variables.
Determine fuzzy sets.
Elicit and construct fuzzy rules.
Encode the fuzzy sets, fuzzy rules and procedures to perform fuzzy inference into the expert system.
Evaluate and tune the system.

3. Example 1: Air Conditioner
Consider an air-conditioner, which has five control switches: COLD, COOL, PLEASANT, WARM and HOT.
Linguistic variable: Temperature
Linguistic Values: COLD, COOL, PLEASANT, WARM and HOT
The corresponding speeds of the motor: MINIMAL, SLOW, MEDIUM, FAST and BLAST.
Linguistic variable: Speed
Linguistic Values: MINIMAL, SLOW, MEDIUM, FAST and BLAST

4. Temperature Graduations
Temp (0C).
COLD
COOL
PLEASANT
WARM
HOT Y* N 5 Y 10
12.5 15
17.5 20
22.5 25
27.5 30
Y : temp value belongs to the set (0<A(x)<1)
Y* : temp value is the ideal member to the set (A(x)=1)
N : temp value is not a member of the set (A(x)=0)

5. Temperature Fuzzy Sets
Linear membership functions

6. Analytical Expression of the Temperature
COLD:
for 0 ≤ t ≤ 10 COLD(t) = – t /
COOL:
for 0 ≤ t ≤ COOL(t) = t / 12.5
for 12.5 ≤ t ≤ COOL(t) = – t /
etc…
all based on the linear equation:
y = ax + b

7. Speed Graduations Speed (RPM) MINIMAL SLOW MEDIUM FAST BLAST Y* N 10 YY* N 10 Y 20 30 40 50 60 70 80 90
100
Y : speed value belongs to the set (0<A(x)<1)
Y* : speed value is the ideal member to the set (A(x)=1)
N : speed value is not a member of the set (A(x)=0)

8. Speed Fuzzy Sets
Linear membership functions

9. Analytical Expression of the Speed
MINIMAL:
for 0 ≤ v ≤ 30 MINIMAL(v) = – v /
SLOW:
for 10 ≤ v ≤ 30 SLOW(v) = v / 20 – 0.5
for 30 ≤ v ≤ 50 SLOW(v) = – v /
etc…
all based on the linear equation:
y = ax + b

10. Fuzzy Rules The rules governing the air-conditioner are as follows:
IF TEMP is COLD THEN SPEED is MINIMAL
RULE 2:
IF TEMP is COOL THEN SPEED is SLOW
RULE 3:
IF TEMP is PLEASANT THEN SPEED is MEDIUM
RULE 4:
IF TEMP is WARM THEN SPEED is FAST
RULE 5:
IF TEMP is HOT THEN SPEED is BLAST

11. Example 2: Determining # of Spare in a Service Center
A service center keeps spare parts and repairs failed ones.
A customer brings a failed item and receives a spare of the same type.
Failed parts are repaired, placed on the shelf
If the required spare is available on the shelf, the customer takes it and leaves the service center.
However, if there is no spare on the shelf, the customer has to wait until the needed item becomes available.
The objective here is to advise a manager of the service center on certain decision policies to keep the customers satisfied.

12. 1. Specify the Problem and Define Linguistic Variables
n: the initial number of spares
m: the customer’s mean delay
s: number of servers
ρ: repair utilization factor
Ratio of customer arrival rate to customer departure rate, or
Ratio of item’s failure rate to repair
Manager tries to keep it high, to increase the productivity
Three inputs: m, s and ρ
One output: n
In other words, a manager of the service center wants to determine the number of spares required to maintain the actual mean delay in customer service within an acceptable range.

13. 1. Specify the Problem and Define Linguistic Variables
Inputs

14. 1. Specify the Problem and Define Linguistic Variables
Output

15. 2. Determine Fuzzy Sets

16. 2. Determine Fuzzy Sets

17. 3. Elicit and Construct Fuzzy Rules
A very basic Fuzzy rule set
suppose: m and s are fixed values
relation between the repair utilisation factor ρ, and the number of spares n

18. 3. Elicit and Construct Fuzzy Rules
Relation between s (number of servers) and m (mean delay):
It is often convenient to represent fuzzy rules in a matrix form, so-called fuzzy associative memory (FAM).
3*3 FAM that will represent the rest of the rules in a matrix form:

19. 3. Elicit and Construct Fuzzy Rules
The cube 3*3*3 FAM representation

20. Rule Table

21. Matlab Fuzzy Toolbox Fuzzy CLIPS …
4. Encode the Fuzzy Sets, Fuzzy Rules and Procedures to Perform Fuzzy Inference into the Expert System
Matlab Fuzzy Toolbox
Fuzzy CLIPS …

22. 5. Evaluate and Tune the System
3D plot of the rules