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composition'. By doing so, confirmed diagnoses, diagnostic hypotheses, and ex-
cluded diagnoses were determined. This diagnostic process was very successful
in partial tests. For instance, in a study of 400 patients with rheumatic diseases,
CADIAG-II yielded the correct diagnosis in 94.5% ([4, p. 264])
Fig. 3.6
S- and Z-shaped graphs of membership functions of the fuzzy sets never,
sel-
dom
,
often
,
always
, etc.
(Modified after [1, p.
145].)
They are fuzzy sets over the uni-
verse of discourse
representing the values of the numerical variable
joint_occurrence
of two events on the
x
-axis, e.g. cough and bronchitis. The value μ
τ
(
x
)
on
the
y
-axisisthemembershipvalueof
x
∈{
0
,
1
,
2
,...,
100
}
in a fuzzy set denoted by the term
τ
i
∈
T
(Joint_Occurrence) such as “seldom”, “often”, etc.
Ω
=
{
0
,
1
,
2
,...,
100
}
When Sadegh-Zadeh had been asked about his view on the development of Com-
puter and AI support in Medicine, his answer was surprising: “Ledley and Lusted
in their seminal paper (1959), and Lusted in his subsequent book, gave rise to the
emergence of the discipline Medical Decision-Making (MDM) that goes under the
same name still today. They introduced probability theory, especially Bayes's The-
orem, logic, and utility theory into medicine as a basis for clinical reasoning. In
the meantime it has become a serious scientific field. But it has remained a theo-
retical field rather than a practical one. In the 1970s, the focus of research shifted
from numerical-probabilistic approach to knowledge-based techniques that came to
be known as (medical) expert systems or knowledge-based systems research. They
were pioneered by early artificial intelligence systems such as DENDRAL, an expert
