Expert System with Certainty Factors (CFs)
The Following CFs are added to the previously described rule based ES for the "lights out" scenario.
Facts collected from data gathering:
old: the lightbulbs are more than one year old {cf 0.2}
sounds: the lightbulbs make rattling sounds when you shake them {cf -0.8}
M-F: it is Monday to Friday {cf 1}
before 5: it is before 5:00 pm {cf 0.8}
Rules:
IF the lightbulbs are more than one year old {cf 0.8}
THEN the lightbulbs are in danger of burning out
IF NOT the lightbulbs are more than one year old {cf 0.8}
THEN NOT the lightbulbs are in danger of burning out
IF the lightbulbs are in danger of burning out {cf 0.9}
AND IF the lightbulbs make rattling sounds when you shake them
THEN the lightbulbs are burned out
IF NOT the lightbulbs are in danger of burning out {cf 0.7}
THEN NOT the lightbulbs are burned out
IF NOT the lightbulbs make rattling sounds when you shake them {cf 0.9}
THEN NOT the lightbulbs are burned out
IF the lightbulbs are burned out {cf 1}
THEN the lights went out because the lightbulbs burned out (R1)
IF NOT the lightbulbs are burned out {cf 0.8}
THEN the power is out in POST
IF the power is out in POST {cf 0.9}
AND IF NOT the electrician is available
THEN the lights went out because the power was out and the electrician was not on duty (R2)
IF the power is out in POST {cf 0.8}
AND IF the electrician is available
THEN the lights went out because the power was out and the electrician was not skilled (R3)
IF it is a workday {cf 0.9}
AND IF it is before 5:00 pm
THEN the electrician is available
IF NOT it is a workday {cf 1}
THEN NOT the electrician is available
AND IF NOT it is before 5:00 pm {cf 1}
THEN NOT the electrician is available
IF it is Monday to Friday {cf 1}
THEN it is a workday
IF NOT it is Monday to Friday {cf 1}
THEN NOT it is a workday
Example interpretations of the given CFs
Q: Was it before 5:00 pm when the lights went off in POST 303D?
A: I didn't look at my watch, but I'm pretty positive that it was before 5:00 pm.
⇒ it is before 5:00 pm {cf 0.8}
Q: Were those lightbulbs more than one year old?
A: Not sure. It's possible.
⇒ the lightbulbs are more than one year old {cf 0.2}
The forward chaining data-flow diagram for this system is illustrated as below.
With these given CFs and the ones collected from the data gathering process, we can calculate the CFs of the rest of the events in this ES.
in danger: {cf 0.16 = 0.2 × 0.8}
NOT in danger: {cf -0.16 = -0.2 × 0.8}
burnt: {cf -0.72 = min[0.16, -0.8] × 0.9 }
NOT burnt: {cf 0.685 = (0.8 × 0.9 + (-0.16) × 0.7) / (1 - min[|0.8 × 0.9|, |(-0.16) × 0.7|])}
power's out: {cf 0.545 = 0.685 × 0.8}
workday: {cf 1 = 1 × 1}
NOT workday: {cf 1 = -1 × 1}
available: {cf 0.72 = min[1, 0.8] × 0.9}
NOT available: {cf -1 = -1 × 1}
R1: {cf -0.72 = -0.72 × 1}
R2: {cf -0.9 = min[0.545, -1] × 0.9}
R3: {cf 0.438 = min[0.545, 0.72] × 0.8}
In summary, with the given set of certainty factors, we are able the derive the certainty levels of different possible conclusions. Specifically, R2 with CF -0.9 is the most unlikely reason in the lights-out scenario, while R3 with CF 0.438 is the most likely reason.
