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However, since only independent variables are available, we first generate ten-
tative data points for the fittings, and these data vectors are regarded as being our
dependent variables. Hence, we may in fact apply the foregoing switching regres-
sion models. In practice these points are parameters in genetic algorithm optimiza-
tion and we aim to find such parameter values that the corresponding data vectors
are good dependent variables. In very large data sets we may first specify these
fittings with a smaller number of parameters and then use the obtained fittings for
the original data set. We may also modify first our original data set by using their
standardized values instead, if necessary for simplifying our task. This clustering
approach is studied more in a separate paper in the near future.
Fig. 18.20 The fitting curve which represents a cluster center in a 2-D space (left), and the
corresponding fuzzy relation with its degrees of cluster membership (intensities, right)
18.6
Conclusions
We have considered above how fuzzy reasoning may be applied to statistical anal-
ysis in medicine. From the standpoint of the philosophy of science, Zadeh's fuzzy
extended logic seems to provide a firm basis for operating with imprecise entities
and approximate reasoning in the medical research. Thanks for this approach, we
may apply approximate scientific reasoning, theories and explanations, as well as
approximate hypothesis verification to our studies. We may also utilize imprecise
and linguistic variables, scales, values and relations in data analysis.
At a general level, in medical statistical analysis fuzzy systems, as well as neuro-
fuzzy and genetic-fuzzy systems, may replace or enhance many traditional methods.
In particular, the traditional methods are often too coarse due to their linear or para-
metric nature, and these cause various limitations for their usage because the real
world is usually non-linear by nature. Typical analyses for fuzzy modeling are anal-
ysis of variance, analysis of covariance, various regression models, cluster analysis,
discriminant analysis and time series analysis. Additional examples would be prin-
cipal component and factor analysis.
Fuzzy cognitive maps, in turn, could often
replace canonical correlation methods.
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