In yesterday's NYT magazine, Peter Maas has an article called "The Breaking Point", which features the concerns of Matthew Simmons about Saudi oil reserves, and puts Simmons' report of Saudi "fuzzy logic" to important rhetorical use:

Two years ago, Simmons went to Saudi Arabia on a government tour for business executives. The group was presented with the usual dog-and-pony show, but instead of being impressed, as most visitors tend to be, with the size and expertise of the Saudi oil industry, Simmons became perplexed. As he recalls in his somewhat heretical new book, ''Twilight in the Desert: The Coming Saudi Oil Shock and the World Economy,'' a senior manager at Aramco told the visitors that ''fuzzy logic'' would be used to estimate the amount of oil that could be recovered. Simmons had never heard of fuzzy logic. What could be fuzzy about an oil reservoir? He suspected that Aramco, despite its promises of endless supplies, might in fact not know how much oil remained to be recovered.

We can deduce from Simmons' ignorance of "fuzzy logic" that he hasn't bought a rice cooker recently. Not that buying a fuzzy logic rice cooker, or riding in a fuzzy logic elevator or a fuzzy logic subway train, would offer much insight into what the term really means. Of course, he could have checked with Google or looked at the Wikipedia entry.

On the other hand, looking the term up might not have helped. According to Simmons' book, when he asked the Aramco manager "what fuzzy logic precisely [means]", he got the standard sort of answer describing the work of Lotfi Zadeh on the logic of statements that are not crisply true or false, but are true to some intermediate degree. Thus the various Saudi oil fields, he was told, are neither exactly young and vigorous, nor old and played out, but somewhere in between. Simmons was not impressed by this answer, and writes that "hearing the Aramco manager's comment was one of the little events that tipped my thinking about the Saudi Arabian Oil Miracle towards skepticism". In fact, I suspect that the "fuzzy logic" presentation in fact was based on relatively sensible methods (though I have no idea whether Simmons skepticism about Saudi oil projections is justified on other grounds or not).

This SF Chronicle story "Rice goes digital cooked the fuzzy logic way" gives a similar sort of formulation:

Fuzzy logic recognizes more than simple true and false values; it sees degrees of truthfulness, for example, in the statement, "There is a 25 percent chance of rain today." Fuzzy logic deals with complex real systems. The Japanese learned exactly how well it worked when they used fuzzy logic to operate subway cars, which then ran and stopped more smoothly than when they were human-operated or automated. Fuzzy logic balanced out the complex components of acceleration, deceleration and braking.

Rice cooks in basically four stages: It stands in water, it boils, it absorbs (the "steamed stage") and then it rests. Heat is accelerated or decelerated for each stage and in different ways for each variety of rice.

This also is likely to leave a logical reader somewhat puzzled. Why are the complexities of subway car operation, or the four stages of rice cooking, improved by an approach that treats propositions as (say) 25% true?

I learned about Zadeh's fuzzy logic when I was a graduate student, back in the paleolithic era, but despite the intrinsic interest of the idea, there didn't seem to be any really impressive results or really useful applications. When I first heard about "fuzzy logic" control systems (during the neolithic age, about 20 years ago -- before Google or Wikipedia), I was puzzled. What exactly does the degree of truth of statements have to do with algorithms for controlling trains or elevators? When I asked this question after a dog-and-pony show at a Japanese research lab in the mid-1980s, I got answers like those that Simmons and the SF Chronicle got, repeating what I already knew about fuzzy logic, without adding anything convincing about the application to control theory. It sounded to me like technological double-talk. I was sure that the engineers were doing something relevant to control in complicated situations, but the "fuzzy logic" label seemed like a flack's evocative slogan for a variety of different technologies that didn't seem to have anything much to do with logic, fuzzy or otherwise.

A friend with a background in chemical engineering set me straight. His explanation went something like this: Standard control systems are *linear*. That means that controllable outputs (heating, accelerating, braking, whatever) are calculated as a linear function of available inputs (time series of temperature, velocity, and so on). Linearity makes it easy to design such systems with specified performance characteristics, to guarantee that the system is stable and won't go off into wild oscillations, and so on. However, the underlying mechanisms may be highly non-linear, and therefore the optimal coefficient choices for a linear control system may be quite different in different regions of a system's space of operating parameters. One possible solution is to use different sets of control coefficients for different ranges of input parameters. However, the transition from one control regime to another may not be a smooth one, and a system might even hover at the boundary for a while, switching back and forth. So the "fuzzy control" idea is to interpolate among the recipes for action given by different linear control systems. If the measured input variables put us halfway between the center of state A and the center of state B, then we should use output parameters that are halfway between state A's recipe and state B's recipe. If we're 2/3 of the way from A to B, then we mix 1/3 of A's recipe with 2/3 of B's; and so on.

In the case of the four stages of rice cooking, I suppose that a fuzzy logic controller is able to treat the process as a series of fuzzy or gradient transitions rather than a series of hard, stepwise transitions. I suspect that Simmons' Aramco executive was trying to present research that used a vaguely analogous method to fit a smoothed piecewise linear model to data about oil recovery as a function of various independent variables, including oil field "age". In both cases, the fuzzy approach might well be appropriate, under whatever name (though here's an alternative story about heating control -- and I have to say that I'm still quite happy with my old non-fuzzy thrift shop rice cooker...).

If you've shopped for a rice cooker recently, you'll have seen the addition of yet another buzzword: some cookers are not just "fuzzy", they're "neuro fuzzy". That term has a "what is this applicance doing to my brain" vibe that may not appeal to Americans -- I notice that our malls are not yet flooded with neuro fuzzy microwaves, for example. And indeed even plain *fuzzy* is by no means an entirely positive word. When George Bush famously accused Al Gore of "disparaging my [tax] plan with all this Washington fuzzy math", it was not a warm fuzzy moment.

But if you want to understand what "neuro fuzzy" means, you can read about it here. And there is a whole fuzzy world out there, as these links can help you discover. Though you might want to read this semi-skeptical review first.

[Update: Fernando Pereira emailed

Petroleum geologists have been pioneers on pretty sophisticated spatiotemporal estimation and smoothing techniques, for instance kriging (aka Gaussian process regression for statisticians). There are tight connections between GP regression and spline smoothing (via the theory of reproducing kernel Hilbert spaces). Either the Saudis are not hiring the best petroleum geologists, or they are being deliberately obfuscating with marketroid talk. I can't think of any situation in which fuzzy ideas (pun intended) would be preferable to Bayesian statistics for inference.

Well, if the "fuzzy logic" stuff in this case was for marketing purposes, it clearly had the opposite of the desired effect on at least one of its targets.]

[Update #2: Mike Albaugh emailed links to an interesting review article by Daniel Abramowitch, with an associated set of slides. ]

Posted by Mark Liberman at August 22, 2005 12:53 PM