# Fuzzy Logic zeitgeist, with statistics

I decided to sift through the cache of alerts ... to get a better idea of the

zeitgeistof fuzzy logic. ...[F]uzzy logic is familiar enough to be used intelligently or casually, and, it turns out, to be chronically misrepresented as well.

In April of this year I subscribed to Google Alerts for the search term "fuzzy logic", for the purpose of marketing research. Byte Craft Limited offers a C preprocessor for fuzzy logic named Fuzz-C. As well, as an engineering groupie and recovering arts student, I've found fuzzy logic an interesting and accessible form of advanced mathematics.

The quickest of primers: Fuzzy Logic is a superset of typical logic that embraces degrees of truth between absolutely `true`

and `false`

. In operation, a fuzzy logic system relates *linguistic variables* in a series of fuzzy rules. Through these variables, *crisp* input numbers get transmuted into a universe of fractional values between 0 (false) and 1 (true), combined in useful ways, and transmuted back as output; the hint of science fiction in this is part of the charm for me. There are many ways to make use of this: you can embed information in the *fuzzy sets* that determine degrees of membership for crisp numbers, and you can embed other information in the fuzzy rules that relate variables.

Alerts on fuzzy logic have arrived steadily, showing that Google is picking up new or newly-rediscovered references to fuzzy logic from the internet. The alerts make interesting morning reading.

Recently, the newsgroup `comp.ai.fuzzy`

discussed the question "What is the actual status of fuzzy logic?". Kaizen, the poster asking the question, wondered if fuzzy logic was a bubble [now burst] and if the golden age of fuzzy is over. Several writers responded that fuzzy is not dead, that it is used widely, effectively, and without fanfare. Some of us thought that the bubble was only in terms of hype; I had recently finished one of the books about the genesis of the number zero, and added that it too probably went through a rush of popularity when it was first made public.

I decided to sift through the cache of alerts that I had archived to get a better idea of the *zeitgeist* of fuzzy logic. The results reflected the tone of the previous discussion: that fuzzy logic is familiar enough to be used intelligently or casually, and, it turns out, to be chronically misrepresented as well.

## Frugal Analytics

A Google Alert is a short email with a list of references to online resources newly indexed by Google, selected for a particular search term or query. (Edit: in fact, they represent changes in the top results for the search term; given the importance of ranking, they might as well be newly indexed.) Each entry gives some context and a link to the text, and the title and general link to the containing site. Some are references to newsgroups or Google's own news service.

I read each resource in turn, and scored it in two ways. The first was a simple check whether or not each resource referred to fuzzy logic proper (or fuzzy in an AI or application context). If it was clear that fuzzy logic was being discussed as a system of logic based on values spanning from fully true to fully false, they were "about fuzzy". If they used the term metaphorically, in an obviously inappropriate context or as a pejorative, there were "not about fuzzy".

To get another axis of representation, I scored each resource on an ersatz continuum:

*Specific details*- The resource detailed essential qualities of fuzzy logic, such as fuzzy zero or one. Details about Lotfi Zadeh's work or Bart Kosko's books also qualified.
*Generic details*- The resource described fuzzy logic in a way that hinted at the basic concepts, but didn't offer enough information for the reader to understand its importance without further pursuit. Simple mention of Zadeh or Kosko fell here.
*Name only*- The resource mentioned "fuzzy logic" as a feature or a detail, appropriately but without any other information.
*Pejorative*- The resource used the term "fuzzy logic" to describe undesirable imprecision, or weak thinking or arguments.
*Other*- The resource used the term "fuzzy logic" in a metaphorical, artistic or throw-away manner, without any indication of understanding fuzzy logic itself.

I also split off all alerts about blogs that used the term in their title, as these caused an alert every time that Google caught new content whether the term appeared in the actual information or not.

Before presenting any results, I must emphasize that this is the most informal of studies. I started with the Google text, and looked at a resource using the attached link if I couldn't take a decision based on the excerpt. I did so for about a third of the resources, finding that, in a few cases, the materials had expired or had been removed. Scoring left a good deal to my own affective judgement and mind-reading capabilities. I went through the scoring twice, but at a fair clip.

## Through Google-coloured glasses

There were 229 newly indexed resources sent as alerts since April. 26% were blog-related updates; I excluded them after a cursory check to see if they had actual fuzzy logic information. Thirteen blogs were represented that used fuzzy logic in their title or domain name. None of them dealt with fuzzy logic itself.

From the remaining resources, 29% dealt with fuzzy logic as a scientific concept or practical application, either as part of or the entirety of the text. `comp.ai.fuzzy`

appeared frequently, as did some of the usual market participants. The balance of these resources, or 71%, had nothing to do with fuzzy logic as practitioners understand it.

Looking at the non-blog resources along the "continuum" of specificity this time, 21% had "specific details" about fuzzy logic. These were texts about fuzzy logic, course or tutorial notes, or detailed reports of new or existing products. 20% had "generic details", which conveyed notable information about fuzzy logic through context or implication but did so inexpertly, like the evening news might do.

21% gave fuzzy logic by name alone. Most of the advertisements about rice cookers appeared here. They mentioned fuzzy logic in an germane way but as a marketing bullet and nothing more. By contrast, 24% used fuzzy logic as a pejorative, and the greatest part of these were political arguments. Even as the alerts first came in I noticed the volume of accusations of "fuzzy logic" used to throw doubt on an opponent's argument. It's too bad that this legacy has attached itself to fuzzy; around here we often resort to the alternative term "linguistic variables", but it's a less euphonic and less all-encompassing term.

The remainder (at 15%) were non-canonical, non-pejorative, unique uses of the term. Artistic uses, such as album or artwork titles or the name of a dance troupe, appeared here. A few people used variants of fuzzy logic as their user IDs online.

Please note: totals do not add to 100 due to rounding. I didn't ignore rigour completely.

## Conclusions

Roughly speaking, for every three "new" mentions of the term "fuzzy logic", one has some glimmer of its canonical meaning or practice. That shouldn't be too surprising on an internet with an academic heritage, but it reveals a healthy awareness of fuzzy logic among content creators.

Looking at the world along the other axis, three out of five mentions of fuzzy logic use the term constructively. One out of five is conversant enough to evangelize for or against it, and two others may be thought of as vaguely supportive or critical. A minority say "fuzzy logic" in contempt or indifference, without caring or comprehending what it is as a science and as a tool.

Some will rightly find fault with my method: that a population of samples is spread quite evenly over a range of categories suggests a bad method of choosing categories or scoring. I don't profess to be an expert at this. Perhaps an evenly distributed result simply means that fuzzy logic has grown to the point of enjoying a stable variety of use and misuse. It's part of the unremarkable mainstream and for this is in no danger of disappearing.

Or I could hope that a much larger sample size would reveal hidden subtleties. I plan to revisit this topic in a year's time and see how a much larger body of indexing describes the latest developments in fuzzy logic.

Kirk Zurell

kirk@bytecraft.com