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With the success of Fuzzy Control in the 1980 the theory of Fuzzy Sets and Systems
became more and more popular. This is often traced back to the implementations of
the fuzzy control principles for products in the household appliance and entertain-
ment industries. But there is another historical pathway of Fuzzy Sets and Systems
that opened out into the medical sciences.
In 1969 Zadeh found that the field of medical sciences was a promising possible
field of application for his new mathematical theory: “Specifically, from the point
of view of fuzzy set theory, a human disease, e.g., diabetes may be regarded as a
fuzzy set in the following sense. Let
X
x
denote the collection of human beings.
Then diabetes is a fuzzy set, say
D
,in
X
, characterized by a membership function
μ
D
(
=
which associates with each human being
x
his grade of membership in the
fuzzy set of diabetes” ([7], p. 205). He formulated these proposals very accurately
and pointed: “In some cases, it may be more convenient to characterize a fuzzy set
representing a disease not by its membership function but by its relation to various
symptoms which in themselves are fuzzy in nature. For example, in the case of dia-
betes a fuzzy symptom may be, say, a hardening of the arteries. If this fuzzy set in
X
is denoted by
A
, then we can speak of the fuzzy inclusion relation between
D
and
A
and assign a number in the interval
x
)
to represent the 'degree of containment'
of
A
in
D
. In this way, we can provide a partial characterization of
D
by specifying
the degrees of containment of various fuzzy symptoms
A
1
,...,
[
0
,
1
]
A
k
in
D
.Whenar-
ranged in a tabular form, the degrees of containment constitute what might be called
a containment table.” ([107], p. 205)
Maybe the first scientific work on Fuzzy sets in Medicine was the dissertation
Fuzzy Sets and Their Applications to Medical Diagnosis and Pattern Recognition
[5] that Merle Anne Albin wrote already in 1975 under Berkeley mathematics pro-
fessor Hans-Joachim Bremermann (1926-1996), a friend of Zadeh's. Unfortunatley
its bibliography does not include any of the texts by Zadeh. Zadeh's aforemen-
tioned works with comments about possible applications of fuzzy sets in medicine
likewise went unnoticed both by Harry Wechsler in his 1976 article “Applications
of Fuzzy Logic to Medical Diagnosis” [91] and by Alonso Perez-Ojeda in his M.S.
thesis
Medical Knowledge Network. A Database for Computer Aided Diagnosis
[54], led to his paper with Moon, Jordanov and Türksen [51]. Petre Tautu and Gus-
tav Wagner, with their aforementioned review article [86], and Richard C. Elder and
Augustine O. Esogbue also failed to mention them in the two parts of their paper
[24, 25] from 1979 and 1980 about a fuzzy model for medical decision making pro-
cesses, which traced back to Elder's M.S. thesis Fuzzy Systems Theory and Medical
Decision Making. [23]
All of these works dealt with the application potential of Fuzzy Set Theory in
the medical field without making any mention of Zadeh's explicit comments on
this subject. They fuzzified medical laboratory findings that were classified either
as normal or as pathological; they established continuous transitions, for instance,
from shortened to normal to prolonged bleeding times or from slightly elevated to
severely elevated cholesterol level corresponded more to a medical mindset. Using
membership functions, values were established to state the degree to which the test
results belonged to the respective fuzzy sets.
[5, 24, 25, 51, 86] They suggested
