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Experts at the Department of Medical Computer Sciences, the University of Vi-
enna Medical School, Vienna General Hospital, had proposed the development of a
computer-assisted diagnostic system that did not use stochastic methods. “It was
intended to develop a system which is not based on statistical assumptions like
normal distribution, mutual independency of symptoms, constant probabilities of
symptoms in different populations and at different observation times. There is no
need for information about the frequency or lack of certain symptoms with the sick
or the healthy. Therefore, rare complaints are considered as well as frequent dis-
eases” ([1, p. 141]). To systemize and formalize medical knowledge and to store
it in a suitable form, the head of the University Department of Medical Computer
Sciences and simultaneously head of the University Clinic of Gastroenterology and
Hepatologymedical Georg Grabner (1923-2006) and the IBM computer scientist
Walter Spindelberger (1929-2011) started to use a computer for medical diagnosis
in the late 1960s. Motivated by the work of Ledley and Lusted this was followed by
intensive collaboration between physicians and mathematicians and engineers and
in 1968 they constructed a first computer-assisted diagnostic system [82]. One year
later Grabner and co-workers published their first experiences with this system for
the differential diagnosis of hepatic diseases [30].
The second generation (called CADIAG-I) was developed in the 1970s on the
basis of three-valued logic [2] and ten years later the “Fuzzy version” CADIAG-
II appeared, based on the conjecture that “Fuzzy set theory with its capability of
defining inexact medical entities as fuzzy sets, with its linguistic approach provid-
ing an excellent approximation to medical texts as well as its power of approx-
imate reasoning, seems to be perfectly appropriate for designing and developing
computer-assisted diagnostic, prognostic and treatment recommendation systems.”
([3, p. 203]).
In the “fuzzy logical model”, published by Klaus-Peter Adlassnig (born 1950) all
symptoms S i
S are considered to be fuzzy sets of X with membership functions
m S i (
x
)
,forall x
X , indicating the strength of x 's affiliation in S , and all diagnoses
D j
D are considered to be fuzzy sets in the set P of all patients under consid-
eration with m D i (
assigning the patient p 's membership to be subject to D j .To
describe “medical knowledge” as the relationship between symptom S i , and diag-
nosis D j , Adlassnig found two fuzzy relations, namely occurrence (How often does
S i , occur with D j ?) and confirmability (How strongly does S i , confirm D j ?) ([3,
p. 225]). These functions could be determined by (a) linguistic documentation by
medical experts and (b) medical database evaluation by statistical means, or a com-
bination of both. In both ways, to determine these fuzzy relations between symp-
toms and diagnoses, occurrence and confirmation, they have been defined as fuzzy
sets. When physicians had to specify these relationships by the exclusive use of the
terms always , almost always , very often , often , unspecific , seldom , very seldom , al-
most never and never , they choose fuzzy sets defined by Adlassnig's determination
of their membership functions (see Fig. 3.6). In the case of medical databases the
membership function's values of occurrence and confirmability could be defined as
relative frequencies. CADIAG-II can infer all meaningful fuzzy relations between
S , D , P , and their complements representing 'medical knowledge' by 'max-min
p
)
 
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