Probably the closest representation that we can get to actual human thought, fuzzy logic implies that ideas have grey areas of importance, that they are relatively true or false, and that people can hold different ideas at different levels of truth. And so, can have dualistic thinking patterns.

When fuzzy logic was first introduced, it was done to some amount of hype and fanfare as the Next Big Thing that would revolutionize computing. It never really did this, because that was never the intent. Instead, it is now most widespread amongst control systems, where you want some amount of self-conciousness when it comes to how close you are to the target. Fuzzies are popular in systems such as air conditioners, rice cookers, and light meters.

To create a fuzzy controller for an air conditioner, you set up a number of nodes on your axis, and give them values, i.e. -20 degrees below the set temperature is really cold, -10 degrees is cold, -5 [degrees is cool, 0 degrees is just right, 10 degrees is warm, and 20 degrees is way too hot. You then program the machine to work at different intensities for each of these temperature values. The fuzzy part comes in when the temperature is say, 8 degrees below the set temperature. The machine will determine that it is 40% cool and 60% cold, and respond accordingly.

There has been some interesting research in combining fuzzy logic with that other hyped technology, neural networks. Basically, you can make a neural net train itself to arrange the nodes and intensities of the fuzzy system so that it will give optimal control.

Like proportional control systems, the fuzzy logic controller I have described above can get really hosed if you have some delay in your system's feedback. It can be set to compensate for this by adjusting non-proportionally when the system is close to the target, but there are times when it can still be beaten by the good old PID control.

According to Daniel McNeill and Paul Freiberger in their book Fuzzy Logic, when Lotfi Zadeh coined the term in his 1964 paper that introduced the concept, his choice of the term "fuzzy logic" was a most unfortunate one1.

Since "Fuzzy logic" has been used in the past to mean Bad logic, the concept was attacked from all quarters. This in turn led to the concept being shunned in the United States.

Fuzzy technology was, however, adopted quite readily in non-Anglophone nations such as Japan2 and Denmark, in whose translation something was perhaps gained.

1The authors suggest that the term multivalue logic would have made a better choice.

2Simulacron3 ret^Hports that the Japanese, at least, missed the chance to come up with a better name: They use a simple phonetic transcription that sounds something like 'fah-jee row-jeek', which gets shortened to just 'fah-jee', reminiscent of fudgy.

Debut album from Welsh band Super Furry Animals, released in May 1996. Hit the giddy heights of number 23 in the UK album charts. Contains the first attempt of the band to sing in English as opposed to their native Welsh. The Super Furries sound stems from the prog-rock versus punk rock collision of guitar-pop, abetted by their early days as a techno band. The album cover features a series of passport photographs of the various identities used by cannabis smuggler, Howard Marks.
1. God! Show Me Magic

Immediately loud, an atheist's anthem, with rinky-dink piano in the background helping to push the beat along. Comes in under two minutes long, ending with screams. One of the singles from the album.

2. Fuzzy Birds

Typical stoners song, the lyrics concern a dream the guitarist Bunf has with his hamster. Can a hamster wheel provide electricity? Under two minutes again, this song is slower than God!, features a nice flute solo and has a nice hummable pop tune.

3. Something For The Weekend

More drugs references, this time profiling the highs and lows of LSD. Got a great chorus, sounds a bit like Blur, this became the band's first top twenty single. Ends with the nagging repeating refrain of "I just keep repeating myself", dragging the song over the two minute mark.

4. Frisbee

More guitar pop, and more lyrically strangeness. A Bruce Forsyth catchphrase gets turned into a lagging terrace chant like chorus. More oohs and ahhs get layered over and above the main lyric and guitars.

5. Hometown Unicorn

The first SFA song I ever heard. The first single released from the album. Slowest song so far, contains another nagging memorable chorus and a fab guitar solo. Song is about alien abduction, specifically the case of Frank Fontaine. Mentions of unicorns add to the 70s prog rockish feel. It also finally breaks the three minute mark.

6. Gathering Moss

Slow mournful ballad. A lament by Gruff about the pace of modern life "you and I, united by itemised bills" transforms into a more uplifting ending. Also has some great keyboard sounds and showcases the bands imagination in a hymn to laziness.

7. If You Don't Want Me To Destroy You

Best song about gravity ever? This was the last single from the album but is probably the one most of the record buying public remember. Another great pop song, augmented by orchestra (possibly on loan from E.L.O.?) that kicks in half-way through.

Fairly straight-forward poppy punk number. Two thirds of the way through though Cian goes wild with his box of tricks as the song heads towards a loud frenetic climax, complete with Elvis-like uh-uh-uhs. Before the days of The Man Don't Give a Fuck, this was the band's set closer.

9. Mario Man

Another slower song, this time referencing console games. Nice example of Gruff's world weary vocals and has another nice guitar solo near the end.

10. Hangin' With Howard Marks

Probably the weakest track on the album. Contains more hero-worshipping of Howard Marks, but doesn't really add anything musically to the album. A few nice lyrical touches though.

11. Long Gone

Like Gathering Moss, another slow ballad, but this time a few strings add to the wistful vocals. Then the song meanders while a drunken answering phone message recorded by two friends (one of who is Rhys Ifans of Notting Hill fame) of the band plays in the background.

12. For Now and Ever

Album finishes with a nice beery sing-along "we'll be together, for now and ever", and probably the only song ever to mention weatherwoman Sian Lloyd. Then it ends in chaos as everything gets turned up to 11 and every special effect and button in the studio is turned on.

All songs written by Super Furry Animals. Produced by Gorwel Owen. Recorded at Rockfield Studios, Wales. Released on Creation Records.

#### Fuzzy Logic

as described in the album sleeve notes:-
"in mathematics and computing, a form of knowledge representation suitable for notions (such as "hot" or "loud") that cannot be defined precisely but which may depend on their context. For example, a jug of water may be described as too hot or too cold, depending on whether it is to be used to wash one's face or to make tea. The central idea of fuzzy logic is probably of set membership. For instance, referring to someone 5ft 9in tall, the statement "this person is tall" (or "this person is a member of the set of tall people") might be about 70% true if that person is a man, and about 85% true if that person is a woman. Fuzzy logic enables computerized devices to reason more like humans, responding effectively to complex messages from their control panels and sensors."

bitter_engineer: "Like proportional control systems, the fuzzy logic controller I have described above can get really hosed if you have some delay in your system's feedback...there are times when it can still be beaten by the good old PID control."

This is true of a fuzzy logic controller whose inputs are simply one or more error signals (or the equivalent). A fuzzy controller is incapable of calculating derivatives or integrals of its inputs, and thus is working with less information than a classical linear controller. From a frequency domain standpoint, such a controller has neither poles nor zeroes, so there's no hope of compensating for undesirable system dynamics.

However, it is possible to design a fuzzy logic controller that is equivalent to any PID controller within some arbitrary range, by providing three inputs to the controller--the error signal and its integral and derivative--and choosing the fuzzy sets so that the gains are equivalent to the PID gains in the desired range of equivalence. This can be extended to linear control in an arbitrary number of state variables by providing each state variable (or an estimate) as a controller input.

This method can be used to design a nonlinear controller by starting with a linear design (probably based on a nonlinear model linearized about an operating point), creating an equivalent linear fuzzy logic controller, and then tweaking the controller's operation outside of the linear region. The "tweaking" can be done automatically in a program like Matlab by creating a simulation using the full nonlinear model, defining a performance metric for the simulation, and running an optimization routine to find the controller parameters that result in the best performance. (Subject, as always, to local minima problems.)

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