Information Technology Reference
In-Depth Information
analyzing fuzzy data: one-sample and two-sample t tests, one-way ANOVA, and
factorial ANOVA. These tests are performed to determine whether to reject null
hypotheses about fuzzy population means. (In the referenced papers that introduced
the statistical tests, the expectation of a random fuzzy set is defined in terms of
the Aumann integral at each
α
level; see, for instance, Puri and Ralescu [16] and
Colubi [2]).
Instead of describing the technical details of the procedures, we provide examples
that illustrate how they can be applied to actual problems in medical research. In
Section 19.4, we outline how to extend classical statistical procedures to fuzzy data.
19.3.1
One-Sample t Te s t
Körner [10], Montenegro et al. [13], and González-Rodríguez et al. [8] developed
one-sample methods for hypothesis testing about the fuzzy population mean; the
procedures examine whether the mean of a distribution of fuzzy observations is
different from a fuzzy set specified in a null hypothesis.
Consider the fuzzy set graphed with a black line in Figure 19.3. We can describe
it as a fuzzy set representing a neutral degree of happiness, “neither happy nor un-
happy”. Suppose that we want to know whether the mean degree of happiness of
patients at a hospital is different from this fuzzy set, call it
denote the
mean degree of happiness at the hospital. The null hypothesis H 0 is that
μ 0 .Let
μ
μ 0 = μ
,
and the alternative hypothesis H A is that
μ 0 = μ
.
1
0.8
0.6
0.4
0.2
0
-100
-80
-60
-40
-20
0
20
40
60
80
100
Happiness
Fig. 19.3 A fuzzy set μ 0 representing a neutral degree of happiness, “neither happy nor un-
happy” (shown in black), and hypothetical responses obtained from a hospital (shown in
gray)
 
Search WWH ::




Custom Search