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defining normal glycaemia, we shall use
μ
n
(
x
)=(
x
−
80
)
/
20
+
1when
x
belongs to
[
,
]
(
)=
(
,
)
(
)=
the interval
60
80
,
μ
x
1when
x
is inside the interval
80
120
,and
μ
x
n
n
(
−
)
/
+
[
,
]
120
x
20
1when
x
belongs to the interval
120
140
. The resulting fuzzy-sets
can be observed in figure 20.1:
Fig. 20.1
Fuzzy-sets for representing hypoglycemia and normal glycaemia levels
In this moment we can obtain the following membership degrees for the afore-
mentioned values
x
=
71
,
69
,
46:
μ
h
(
71
)=
0
.
45,
μ
h
(
69
)=
0
,
55,
μ
h
(
46
)=
1
,
0and
(
)=
.
(
)=
.
(
)=
.
μ
0. Now we can see that the “hypo-
glycemia paradox” is solved and only exists under the strict aristotelian logic. For
a concentration of 69
mg
71
0
55,
μ
69
0
45,
μ
71
0
n
n
n
/
dl
of sugar in blood, this value has a membership degree
of 0
45 membership degree to the fuzzy
set of normal glucose levels. Needles to say, a value of 46
mg
.
55 to the fuzzy set of hypoglycemia and 0
.
/
dl
is now correctly
represented, with a 0
.
0 membership degree to the set of normal glucose levels and
1
0 membership degree to the fuzzy set of hypoglycemia.
Kazem Sadegh-Zadeh in his
Handbook of Analytic Philosophy of Medicine
makes the point that “almost everything in medicine is inevitably vague” [8], includ-
ing the following families of health-related concepts: Patient complaints, Symp-
toms, States of the organism, Diseases, Therapies and Recoveries. We not only
agree, but would like to add also Life Illness Curves and Life Quality Curves, as
discussed on the following section.
.
20.3
Life Illness Curves (LIC) and Life Quality Curves (LQC)
We define a Life Illness Curve as a graphical representation of the membership
degree that a person has to the fuzzy set
I
of Illness over time, that is
y
=
μ
I
(
x
)
,
t
.In
these graphics, the vertical axis represents the membership
μ
I
(
x
)
, defined as usually
in the interval
0 means an absolutely absence of illness
that is experienced by the human being only at birth, when no congenital disorder is
present. We emphasize the condition “only at birth” because cellular deterioration
[
0
,
1
]
.Thevalue
μ
I
(
x
)=
