Original post by irbrian
Incidentally, unless its a common usage, I wouldn''t define probability as a range of values [0,1] as that really
Probabilities are most definitely described on the set [0,1]. Percentages and probabilities are NOT the same thing, since a percentage is just talking about a proportion of something. Any decent book on probability theory should be clear about this.
Original post by irbrian
causes some confusion with the whole Fuzzy Logic 0.0-1.0
Yes, it does for many people, which is why these people think it is appropriate to use Fuzzy Logic to describe uncertainty.
Can''t we just use percentages for probability like the rest of the world
At least within the scientific communicty, the ''rest of the world'' does not use percentages instead of probabilities.
Ugh, now you''re trying to turn it back into Fuzzy Logic.
Sorry. I hadn''t slept in a very long time when I read your post. I''m sure I simply misinterpreted what you wrote as you trying to make a disctinction between FL and probability theory using that example. Sorry if it has confused the issue.
but I don''t think even FL should allow two mutually exclusive conditions to co-exist.
Actually, that was the whole point of Fuzzy Logic. One common example used to teach people FL is to ask those people in the audience "put up your hand if you are happy with their job" and then to ask "now put down your hand if you are unhappy with your job". Anyone with their hand still up is displaying Fuzzy Logic in that they are both happy and unhappy with their job. Given only those two statements, it seems nonsensical to be both happy and unhappy about something. But clearly, hidden in that example is the possibility that they are not always happy and unhappy, but rather happy at some times and unhappy at others. The temporal aspect is withdrawn from the premises, allowing the apparently contradictory result.
0-10% --- Invalid Range for Belief formed by AI
10-20% -- NPC Believes the proposition is FALSE
21-40% -- NPC Believes the proposition is "probably FALSE"
41-60% -- NPC Believes the proposition is EITHER True OR False -- NOT True AND False.
61-80% -- NPC Believes the proposition is "probably TRUE"
81-90% -- NPC Believes the proposition is TRUE
91-100% - Invalid Range for Belief formed by AI
But here you''re trying to map a continuous variable to discrete outputs, which is what happens in the final step of Fuzzy Logic (and vice versa for the input). Why is it necessary to do this? If you''re looking for a way of describing confidence in the probability of an event, you might want to use Dempster-Shafer theory. If you''re simply trying to relate probabilities to linguistic statements of belief, the yes, what you''ve done above might be quite reasonable, however it''s also quite arbitrary, so if you said event X was probably true, you would mean that the probability of the event is between 0.61 and 0.8. However, someone else might think that this means the probability of the event is between 0.75 and 0.90, obviously because they use a different mapping function. How do we decide on an ''appropriate'' mapping?