The Construction of Fuzziness - Fuzziness and Medicine - page 14

1. ξ = Ω , A , μ ,

2. is a non-empty set,

3. A is a fuzzy set over

Ω

Ω ,

4. μ is the membership function of A.

That is, a fuzzy structure is a triple Ω , A , μ consisting of a universe of discourse Ω ,

a fuzzy set A over this universe, and its membership function . Now, our question

whether fuzziness exists, reduces to the question whether there are fuzzy structures
as just defined. Otherwise put, are there models for the set-theoretical predicate as
defined in Definition 2? The answer to this question is twofold:

μ

First: No, there are no fuzzy structures in the real world out there because a func-
tion from something to the unit interval such as a membership function μ is an

abstract mathematical construct and does not exist in the empirical world.
Second: But of course, as abstract mathematical structures , fuzzy structures exist.
What is needed for their existence, is only human beings to construct such mem-
bership functions as

. Thus, fuzzy structures and their fuzziness are man-made
formal entities, i.e., artifacts, like numbers in mathematics.

μ

2.5 Concluding Remarks

Medicine as an application domain of fuzzy logic shows how fruitful even an ab-
stract mathematical constcruct like the concept of fuzzy set can be. A few remarks
here may suffice to realize the future impact of fuzzy logic on medicine:
Biomedical research, so-called, comprising cytology, physiology, biochemistry
and other fields usually conducted on animals, is in fact zoology and paramedical
auxiliary. Therefore, it should not be mistaken for medicine. It is true that this
auxiliary paramedical research is based on natural-scientific principles of inquiry
and is therefore a natural science discipline with its own methodology. Medicine as a
healing profession, however, is not a natural science discipline. It is concerned with
the health, illness, disease, therapy, life, and death of the patient as a human being,
i.e., with something that is defined not by nature, but by human values, society,
and culture. Accordingly, the statements that it produces and which control the
behavior of the physician in diagnostic-therapeutic decision-making, are in the main
conditional imperatives of the following form:

If A is B 1 & ··· & Z is B m and you want to achieve the goal G ,

& C n .
Insofar as medical thinking and practice has been concerned with this value-laden
and action-theoretical subject rather than with zoology, it has taken place in a
methodological vacuum until now. Medical students, doctors, and scientists have
never been taught a methodology for their clinical decision-making and research
simply because there is as yet no such methodology in medicine. A major ob-
stacle to its emergence and development has been the fact that medical language
and knowledge are inherently and irremediably vague and, therefore, not amenable

then do C 1 & ···