What is an "If-Then" rule? Can someone give a concise, layman's explanation of an "If-Then" rule (as in rule-based systems).  I am finding this term used frequently without anyone really defining it properly.
 A: It is just a simple classifier; so simple that it is better to explain it by example. Let's say you have a 3 class classification problem and information system with 4 continous predictors $X1,\ldots, X4$. Now you can define simple rules like:
IF X1<3.45 THEN Class1
IF X3>7.2 THEN Class2
IF X2<2.11 THEN Class1
IF X2<1.2 THEN Class3
 ...

and this is it; the final decision is produced by voting. Structures like this can be trained by various methods, probably the best known are rough sets.
A: Actually, I think the given answers are incomplete or inaccurate.
Rule-based systems have a set of IF-THEN rules. These rules are not a "forest" as in a Random Forest. They don't vote. They are all active at the same time and if the IF conditions are met, the THEN fires. The IF parts look into a pool of facts and the THEN parts can insert or retract facts in the pool.
So you can start with 1 fact or dozens of facts, and when no more IF's are true, the process stops. You may then have 0 or more facts remaining -- more or fewer than you started with.
As you might imagine, this can lead to infinite loops. Real-world Rule-based systems have mechanisms for enabling and disabling rules from firing or from firing repeatedly, prioritization of rules, etc. (And in the real world, rules do actually fire one at a time and not simultaneously: they are queued as they become active and dequeued if they become inactive, and the one at the top of the queue is fired at each implicit loop.)
The ordering of the IF-THEN rules may matter to some degree -- which fire first if several are eligible, etc -- but not like a programming language if-then, where order matters a lot and there is no implicit queue/loop of eligible rules.
A: IF - then rule term is generally used in Fuzzy Logic.
This is the main feature of fuzzy logic .
I think you should study the fuzzy logic text for your problem
