MathCAD

Even the reader who hasn't been paying much attention will notice some discrepancies and simpiflications in our analysis of this task. Three of them are:

- Unlike our theoretical bucket, a real one is never filled up right to the brim ("what counts as full?" defines another fuzzy set).
- The author has only loosely defined, and often confused, such concepts as "volume", "weight", and "weight of bucket".
- We haven't taken into account the weight of an empty bucket, and also the material from which it is made.

However it is merely necessary to glance again at the diagrams illustrating fuzzy sets in figs. 6.41, 6.42 and 6.43

to understand a major virtue of applying FST to decision-making tasks. Our solution works in isolation, so it's possible to express the essence of a task disregarding various minor variables: the density of water, weight of the empty bucket, degree of filling, etc. This feature is now realized, for example, in automatic control systems, where regulators based on FST rules are more 'attentive' to the basic signal and less susceptible to noise. It turns out, though it seems paradoxical, that the traditional 'precise' control algorithms qualitatively lose out to 'fuzzy' ones, or are their special cases. In the field of automatic control theory, a certain stagnation could be seen until recently, as any new algorithms couldn't be compared to the older Proportional Integral Derivative (PID) control algorithm. The principles of PID control can be seen in the procedure for a bank's credit check on a client applying for a loan. The banker, in assessing the decision, considers:

1) The sum of money in the client's account (this is the proportional component: the richer the client, the larger the loan that can be offered);

2) The average sum in the account over, say, the last five years (the integrated component; checking this ensures that the client didn't borrow a million pounds the day before, to create the illusion of solvency); and