MathCAD


6.9.6. A genuinely optimum fire bucket - часть 4


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).

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:

  • bucket is light (1);
  • bucket is more light than heavy (0.67);
  • bucket is more heavy than light (0.34):
  • bucket is heavy (0).

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).




- Начало -  - Назад -  - Вперед -