MathCAD

Fig. 6.41. Optimum radius of fire bucket

Step 1 (fig. 6.41). The matrix ?r stores people's views about the optimum (most convenient) base radius r of a conical fire bucket, expressed in millimeters. This data could be gathered by making buckets of various geometries, giving them to people to try out, and then asking for estimates on a scale:

- convenient (1);
- more convenient than inconvenient (0.67);
- more inconvenient than convenient (0.34);
- inconvenient (0).
- bucket is light (1);
- bucket is more light than heavy (0.67);
- bucket is more heavy than light (0.34):
- bucket is heavy (0).

It would be possible to have more options within the range 0-1. In step 1 we have a limited familty of points, but these also could be increased; there are as many opinions as people. Readers can ask all their friends, and add new columns to the matrix [?r]

Step 2. The survey data is processed by the least squares method (see Etude 4). We can see that the data approximately fits a normal distribution curve (see figs. 6.41 and 6.42). The idea of a 'membership function' ?r for the radius of the bucket is one of the basic concepts of FST. In normal mathematics it would be considered that a certain size either belongs, or does not belong, to a particular set; in FST it's permissible to say that the size belongs to the set to some extent

(so many percent).

Step 3. The statistical processing is completed and plotted.

**Fig. 6.42. Optimum height of a fire bucket**

Steps 4-6 (fig. 6.42) repeat steps 1-3, but for a second parameter of the bucket, its height.

**Fig. 6.43. Optimum volume of a fire bucket**

Steps 7-9 repeat steps 1-3 and 1-6 for the third important parameter of the bucket, its volume (or weight – they're proportional). This is based on human estimates:

The survey data is processed as before, but using a "one-sided" cumulative distribution curve (see item 9 in a fig 6.43). (When designing technical systems, such parameters wouldn't be based on a survey but on figures provided by experts to the decision-makers).