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most of the time the evidence is not perfect, at all, even if the classes (subsets) are
assumed to be perfect. The difference between the fuzzy measure and the measure
of fuzziness relies on the fact that for the first the subsets (classes) are crisp not
presenting fuzziness associated to their boundaries. In turn, a measure of fuzziness
concerns the degree of evidence or belief associated to a fuzzy set (input) that a
particular element belongs to a fuzzy set (class), one with unsharp boundaries. As
before mentioned, a fuzzy set is related to each element of the universe of discourse
be assigned a value representing the degree of membership in a fuzzy set and, due
to that, related to fuzziness [12].
In the field of medicine and health care, the difference between fuzzy measure
and the measure of fuzziness can be exemplified as follows. Given an ill patient
and inconclusive evidence obtained by anamnesis or physical examination, how to
classify or diagnosis this individual is not a simple task. If there are predetermined
crisp subsets (classes) of diagnosis, where each individual must be allocated in, a
fuzzy measure is, then, employed. Nevertheless, if the predetermined classes are not
crisp at all and due to that present unsharp boundaries, then it is a matter of using
fuzziness in measurement and approximate reasoning [12].
Table 16.1
Classification of Overweight and Obesity by %BF
Obesity Women Men
Adequate (AF)
<
25 %
<
15 %
Low (LF) 25-30 % 15-20 %
Moderate (MOD) 30-35 % 20-25 %
Elevate (ELEV)
35-40 % 25-30 %
Morbid (MOR)
>
40 %
>
30 %
(Source: WHO - World Health Organization)
Consider, for instance, the clinical guidelines on the identification, evaluation,
and therapeutic conduct of overweight and obesity in adults in Table 16.1 refer-
ring to Percentage of Body Fat (%BF), as assigned by the World Health Organiza-
tion (WHO). Observe that the classifications are crisp sets as depicted in Fig. 16.3
and these crisp classes were modified to fuzzy sets in order to accommodate the
subjectivity in classification, as first presented in [14]. The fuzziness in the fuzzy
%BF obesity classification is shown in Fig. 16.4. This novel approach not only
presents fuzzy %BF classes (input) but fuzzy BMI (Body Mass Index) classes (in-
put) that are aggregated by employing logical connectives for further being mapped
into new fuzzy obesity classes (output), resulting in a new index named Miyahira-
Araujo Fuzzy Obesity Index (MAFOI). Such a novel fuzzy obesity index introduces
fuzziness in the manner to understand obesity and the relation between individu-
als to their obesity condition. MAFOI also establishes a criterion that provides a
mechanism to deal with clinical analysis and syndrome assessment, classification,
therapeutic conduct and surgical (bariatric) indication [16]. The MAFOI is, then,
