Information Technology Reference
In-Depth Information
Fuzzy set theory and fuzzy logic are feasible alternatives to represent the inac-
curate, unclear, uncertain, imprecise, vague information, as well as partial truths -
i.e., imperfect information [19] - inherently associated to clinical aspects of pain
and the subjectivity present in human nature. Different from classical sets, where
an element,
x
, defined in an universe of discourse,
X
, belongs to a set,
M
=
{
x
∈
X
}
,
or not, such that
, fuzzy sets employ membership functions to de-
termine degrees varying from zero to one which an element belongs to a set [18].
A fuzzy set is, then, defined in a universe of discourse,
X
, representing the pos-
sibility, similarity, or conformity an element,
x
, belongs to a set,
M
μ
M
(
x
)
→{
0
,
1
}
=
{
x
∈
X
}
,
according to a degree,
μ
M
(
x
)
, in the interval,
μ
M
(
x
)
→
[
0
,
1
]
.
An element map-
ping to the null value,
0, means that it is not included in the fuzzy set,
while mapping to the unitary value,
μ
M
(
x
)=
μ
M
(
x
)=
1, describes a fully included member,
and mapping into this interval, 0
1, represents a partial degree of mem-
bership. A fuzzy set is characterized by a support,
s
<
μ
M
(
x
)
<
(
M
(
x
))
, and a core,
c
(
M
(
x
))
,
of a membership function,
M
(
x
)
, respectively,
s
(
M
(
x
)) =
{
x
∈
X
|
μ
M
(
x
)
>
0
}
and
c
(
M
(
x
)) =
{
x
∈
X
|
μ
A
(
x
)=
1
}
. While, the first is the set of all elements in
X
that
belongs to the set
M
has positive membership function (are not null), the latter is
the set of all elements whose degree of membership is unitary to the set
M
(
x
)
(
x
)
.
24.2.1
Unidimensional Fuzzy Pain Intensity Scale
The internationally validated and accepted main classic pain intensity measurements
are inherently crisp set representations. To best represent the inherent imprecision,
uncertainty and vagueness related to the fifth vital sign/symptom of medical con-
dition, the visual analog scale (VAS), numerical rating scale (NRS), qualitative rat-
ing scale (QRS), face pain scale (FPS) are extended to fuzzy set theory obtaining
the fuzzy visual analog scale (FVAS), fuzzy numerical rating scale (FNRS), fuzzy
qualitative pain scale (FQPS), fuzzy face pain scale (FFPS) in [3]. The fuzzy pain
intensity scales use possibility distribution functions to represent the inherent im-
precision, uncertainty and vagueness presented in the pain report and assessment.
Fuzzy Visual Analog Scale (FVAS)
The fuzzy visual analog scale consists of a 10 cm single line assigned in one
border labeled
no pain
in opposition to the
maximum pain
in the other extremity
(Fig. 24.1a). The patient marks this line with a cross, trace or any sign concerning
pain intensity. The distance from beginning of the line (zero point) to the mark,
x
,
is directly measured in centimeters by employing a ruler or by a computer program
[5]. The mark in the line corresponds to the core of the membership function and,
thus, to the maximum value of pain intensity,
1. Since there is subjective,
vague representation of the pain in the scale as well as there is no accuracy in uti-
lizing a ruler in centimeters or the reading does not represents accurately the actual
value, then a fuzzy set best represents the mark of the patient Fig. 24.1c. Approxi-
mately 2, and about 5 are, respectively, described by Gaussian and triangular fuzzy
sets.
μ
M
(
x
)=
