Fuzzy Logic

FUZZY LOGIC

I think one way to deal with this is to allow for more nuanced levels of truth. With cookies, the point is that there isn’t just “fine” and “not fine” for amounts of cookies to eat. There is “fine”, “less fine”, “sort of okay but not great”, “not that great”, “dubious”, “suspect”, “a bit much”, “too much”, “way too much”, “ludicrously excessive” and so on. As we saw in Chapter 4, normal logic with the law of the excluded middle doesn’t allow us anything except “fine” and “not fine”, so we end up pushing everything into one or the other as we can’t find a logical place to draw a line. Instead we might try to treat truth values as something on a scale between 0 and 1. This can be dangerous in some situations because it can give the idea that truth is something negotiable, and that some things are more true than others. However, I think this is true in the case of grey areas. It also might be true in the case of probability, when we can’t be certain what the truth is, we can only be a certain percentage sure, with the rest being in some doubt. Percentage probabilities are, in a way, placing things on a scale of truth between 0 and 1. Unfortunately it often seems that we humans are not very good at understanding those either.

In Chapter 4 we briefly mentioned fuzzy logic, a type of formal logic that takes truth values in a range from 0 to 1. This measures the extent to which something is true, rather than our certainty about whether or not something is true. The two things are related, but not exactly the same. For example, if I look up the weather online it gives me a percentage likelihood of rain during each hour of the day. Usually I conflate this with an amount of rain in my head – if the forecast says 90 per cent chance of rain, I interpret it to mean it’s probably going to rain hard. If it says 40 per cent chance of rain, I interpret it to mean it might rain a bit. In practice this is likely to be because of where the uncertainty of a weather forecast comes from. The only way to be really sure that rain is coming is if there is a very strong storm heading strongly in this direction. If we’re not sure, it might be because it’s only a light rainstorm that has some chance of fizzling out or changing direction.

Similarly if an exam is marked with just pass and fail, then the result is very clear cut. Before you get the result you might be unsure about whether you passed or not, but only if you’re a somewhat borderline case. If you’re a really excellent student you might be unsure quite how well you did, but still sure you passed. Again, the certainty and the extent to which something is true are related.

However, even once uncertainty has been eliminated, the extent to which something is true can still vary. If an exam is marked on the whole scale from 0 to 100, you might get a mark of 71 and ask your teacher if that counts as good or not. There is now a whole scale from good to bad, and the uncertainty comes from the grey areas, not from actually not knowing.

Fuzzy logic is currently used more in applied engineering than in maths, to deal with grey areas in the control of digital devices. One example is in rice cookers, where the cooking process can be adjusted according to some slightly vague conditions like whether the water is being absorbed slowly, quite slowly, quite quickly, or quickly. This can also be done for heating or air-conditioning control, or anything else that needs to respond dynamically to potentially changing conditions. Of course, a definition still has to be produced as to what those gradations mean, but having the possibility of truth values in between sheer true and false opens possibilities for more subtle control of devices.