Information Technology Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
-100
-80
-60
-40
-20
0
20
40
60
80
100
Happiness
Fig. 19.2
A fuzzy set representing a perceived degree of happiness
the patient is required to provide a single number (which can be computed from
the single point that she marks) for the inherently imprecise measurement, and it
is unrealistic to assume that the number accurately reflects the perceived degree of
happiness.
Fuzzy sets are effective in encoding the type of measurement described in the
example. Figure 19.2 shows a sample response that represents a perceived degree
of happiness. The horizontal axis represents the degree of happiness; as in the case
of the visual analogue scale described above,
100 represents the greatest degree of
unhappiness, whereas 100 represents the greatest degree of happiness. Clearly, the
patient must be given proper instructions for using a fuzzy set to report her degree
of happiness. For example, the patient must be told to assign 1 to those values in
the interval [
−
100, 100] that are most compatible with his/her degree of happiness.
This fuzzy set reveals the imprecise or uncertain nature of the measurement. Also,
the patient is provided with infinitely many possible responses, and the scale can
capture subtle differences or variability.
Even though fuzzy sets can effectively represent imprecise, uncertain, or linguis-
tic measurements, they would not be useful for statistical studies if they could not be
analyzed statistically. Fortunately, various quantitative procedures are available for
statistically analyzing fuzzy data. We will review some of them in the next section.
−
19.3
Statistical Procedures for Fuzzy Data: A Tutorial
Exposition
Some of the most frequently used classical statistical tests have been successfully
extended to fuzzy data.
In this section, we review the following procedures for
