Fuzzy Logic

portalparts.acm.org

ISBN 0671738437

Fuzzy Logic is type of Many Valued Logic invented by Lotfi A. Zadeh (Zadeh Lotfi) in 1965 (but popularized quite a bit later) in which truth values of variables (Fuzzy Variables) can take any value from 0% to 100%. Contrast with Boolean Logic that treats purely binary logical states: a statement can only be either 100% true or 100% false.

For example, consider the statement "It is warm." The variable warm is a fuzzy variable, and the truth of the statement depends in some way on the relationship between the actual numerical temperature and the person making the statement, and results in some truth level between 0% (it's not at all warm) and 100% (it's quite definitely warm, that's for sure).

Fuzzy Variables and Fuzzy Logic are considered very useful for engineering and computer applications that handle real-world relationships and subjective numbers. Thermostats are always invoked in the examples -- instead of using a Boolean Expression like "If the temperature is 3.8 degrees C higher than the target, then turn on the cooler, otherwise shut it off," one can write a Fuzzy Expression that runs more like "If the temperature is warm, then turn the cooler on low; if the temperature is hot, then turn the cooler on high."

The trick of course is determining what "warm" and "hot" and "low" and "high" mean as Fuzzy Variables, and how they relate to one another -- which is Fuzzy Logic. It involves designing all the Fuzzy Variables so that they map the actual numerical values of temperature and cooler activity onto the classes like "hot" and "cold" and so forth, and also designing a defuzzification method that, once a decision has been made, tells the old-fashioned controller to do something with a real number again.

It should be (and is frequently) noted that "Fuzzy Logic" does not mean "Fuzzy Thinking", even though this is the basis for innumerable sly-sounding jokes by relatively ignorant people. -- Bill Tozier

It's also worth noting that Fuzzy Logic does not contribute truly new mathematics; it has been critiqued because everything it offers has been done for ages with mainstream statistics. However, it has turned out to be nonetheless valuable as a new paradigm; it encourages thinking statistically about problem domains that had previously been typically dealt with in terms of discrete value logic. -- Doug Merritt

I disagree with Doug. In his book Fuzzy Thinking, Bart Kosko demonstrated why fuzzy logic is a superset of statistics, rather than the otherway round. Understanding why requires a rather deep understanding of fuzzy logic, and is rather difficult to explain because Western culture derives from black & white logic (originating with Mr Aristotle). Maybe I'll have a go explaining some time, but Bart Kosko takes half his book to explain fully! -- Chris Handley

I also disagree with Doug Merritt. Probability is a (very practical and useful) special case of Fuzzy Logic. There is a whole range of math behind fuzzy logic and fuzzy sets. Fortunately, the most practical stuff is the simplest. -- Doug Ransom

Perhaps it should be called "probabilistic logic".

[It's already taken.]

Much popularizations of FL are about the fuzzy tiles. They derive from ways mathematicians describe to domain experts how to set coefficients for their formulas.

All we are really talking about here is a response curve whose derivative is continuous. In other words, the curve is smooth, and every point has a closest tangent with an unambiguous slope. That's why using opinions for the input can create FL output that's smooth and not jerky. -- Phl Ip

Fuzzy Logic for Process Control is a neat idea, but it ain't magic. If you thought tuning a PID loop was a pain in the butt, try coming up with the right set of fuzzification/defizzification curves. Either way, it takes practice, patience, simulation, and a bit of luck to get it right.

Just like Genetic Algorithms or any Evolutionary Algorithm for that matter, Fuzzy Logic for Process Control is a Heuristic Rule, and there aren't any good Meta Heuristics yet. You offload the difficulty of solving the problem once it's been posed onto the difficulty of posing the problem in the first place.... All of these heuristics are an Art Becoming Craft. -- Bill Tozier

Fuzzy Logic, however, really shines when there are multiple sensors that control an output. One can describe the effects of the sensors individually and a small set of interactions between sensors (if desired) and then combine the results. Yes, the result may require tuning, but at least it is possible to create a result. -- Wayne Mack

Some links:

Fuzzy Logic Links AI Wiki -- arvo.ifi.unizh.ch

Fuzzy Logic Google Category -- directory.google.com

Fuzzy Logic Archive (since 1994) -- www.austinlinks.com

Fuzzy Logic Newsgroup (since 1993) -- www.cs.cmu.edu

Fuzzy Logic FAQ -- www.abo.fi

Category Fuzzy, Category Logic, Category Information Orientation

See original on c2.com