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a fuzziness approach concerning health, illness, and disease is somewhat contested
meanwhile being in some part acquiesced in [17]. Another provocative philosoph-
ical and methodological approach on employing the fuzzy set theory, degrees of
truth, and subjectivity in epidemiology, in particular, and medicine, in general, is
available in [33]. The fuzzy epidemic approach in [13] endorses the importance of
the fuzzy set theory and fuzzy logic in medicine and health care. The work on the
fuzzy trace theory is also an instigating perception of fuzziness in the prevention be-
havior or in supporting medical decision making as given in [19]. A descriptive use
of fuzziness to medical decision making in Intensive Care Units is reported in [7].
A cognitive presentation on fuzziness in pharmacy, in particular, and medicine, in
general, can be found in the tutorial in [28]. Another source of elucidative papers on
the use of the fuzzy set theory and fuzzy logic in etiology, nosology, and diagnosis
in medicine is within the series [20-24]. Thus, the use of fuzzy sets and fuzzy logic
seem to be appropriate to make computers carry out decision making, emulating
paradigms and mechanisms assumed to be in action in medicine and health care.
The content herein exposed aims at presenting that fuzziness is inherent in mea-
surement and reasoning through the approximate reasoning approach, in general,
and proper for the field of medicine and health care, in particular. In so doing, the
compositional rule of inference and conditional restrictions working as a fuzziness
mechanism of measure are natural approaches for being employed in analysis, as-
sessment, classification, therapeutic conduct.
16.2
Fuzziness in Reasoning and Measurement
When a computer carries out a decision, it relies on emulating paradigms and mech-
anisms assumed to be in action in the human mind. Equivalent in structure, the
classical (Aristotelian) logic and the fuzzy logic differ according to the sort of in-
formation and the inference system. While the classic (Aristotelian) logic is based
on bivalued propositions, describing perfect, crisp reasoning, the fuzzy logic uses
multivalued propositions (infinite levels of truth), describing imperfect, uncertain-
imprecise reasoning (vague, approximate reasoning).
The classic (Aristotelian) logic is based on the
third excluded principle
in which
propositions are assumed to be either true or false. Nevertheless, requiring that
propositions be only true or false is, in numerous situations, to evade the real-
ity, since it requires information be perfect. Most of the information that humans,
systems, or machines deal with are, actually, imperfect, being characterized as im-
precise, uncertain, vague, or that corresponds to either partial truthiness or sub-
jectiveness (Figure 16.1). An alternative to deal with imperfect information is to
employ the fuzzy set theory and fuzzy logic, through the approximate reasoning
approach.
The approximate reasoning is characterized by rules that (
i
) describe a functional
input-output mapping by using linguistic terms, (
ii
) present as fundamental element
the fuzzy graph, (
iii
) incorporate a fuzzy inference that involves a set of fuzzy rules
(fuzzy model), such that the antecedents of the rule form the fuzzy partition of
