Information Technology Reference
In-Depth Information
3.6.6
Similarity of Diseases
Why do we categorize a human condition
H
i
as disease but not human condition
H
j
? Sadegh-Zadeh named “menstruation, pregnancy, tax evasion, smoking, torture,
terrorism” to clarify distinctly: “We do not mean that the latter examples are or have
to be categorized as diseases. We only ask why they are
not
categorized as diseases.
His answer is: “What is called a disease in medicine is representable as a fuzzy
human condition of the form
H
=
{
(
F
1
,
μ
H
(
F
1
))
,
(
F
2
,
μ
H
(
F
2
))
,...,
(
F
n
,
μ
H
(
F
n
))
}
.”
as in equation 3.24. [70, 128]
Already in 2000 Sadegh-Zadeh established the following rules to determine when
human conditions
{
D
1
,
D
2
,...,
D
n
}
are called diseases with respect to their corre-
sponding features (or criteria)
{
C
1
,
C
2
,...,
C
n
}
:
•
Every element
D
i
∈{
D
1
,
D
2
,...,
D
n
}
is a disease.
•
{
,
,...,
}
Every element that is
similar
to a disease with respect to criteria
C
1
C
2
C
n
is a disease.
To define what is meant by
similar
diseases Sadegh-Zadeh used the map
dif-
fer
, i.e. the difference of two fuzzy sets
A
and
B
. As we mentioned in defini-
tions 18 and 19 in subsection 3.5.3, the
similarity
of two fuzzy sets
A
,
B
is resulted
from the inversion of their difference
differ
(
A
,
B
)
. To calculate
similarities
between
fuzzy sets, we use Sadegh-Zadeh's theorem 2 in the list at the end of the subsection
3.5.3, i.e.
(
A
,
B
)
c
(
A
∩
B
)
c
similar
(
A
,
B
)=
.
(
A
∪
B
)
3.7
The Prototype Resemblance Theory of Diseases
Sadegh-Zadeh's line of argument (see subsection 3.6.3) shows that he was not inter-
ested in “similarity-in-general” but in “similarity-in-some-particulars”. To declare
his intent he provided, already in 2000, this example: “a human condition, such as
a myocardial infarction, may be construed as a set consisting of a large number of
attributes, such as myocardial ischemia, arrhythmia, abnormal EEG, elevation of
LDH enzyme, chest pain, fear of death, ..., .... In comparision, another human con-
dition, such as gastric ulcer, may be another set consisting of another large number
of attributes. Although phenomena of these divers kinds are in principle comparable
with one another, they are not easily comparable in their entirety.” [66, p. 623]
To compare such phenomena not as a whole but “only with respect to a partic-
ular set of criteria, that is, with respect to a
comparable subset
of their attributes,”
Sadegh-Zadeh introduced the relationship of
partial similarity
. Thus, if we want
to compare “two large, possibly incommensurable human condition sets
D
i
and
D
j
,
we ask:
everything else left aside
, how similar are
D
i
and
D
j
with respect to the few
criteria”, say,
“they share to varying extends? This kind of simi-
larity confined to particular criteria such as
{
C
1
,
C
2
,...,
C
m
}
is referred to as
partial
similarity
with respect to this set of criteria.” [66, p. 623] To define this relationship
he introduced the following notation:
{
C
1
,
C
2
,...,
C
m
}
