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Nevertheless, since the crisp mark 120 is not liable in all cases as it is a somehow
arbitrary and changing threshold, it could be better to frame the diagnose in the
setting of fuzzy logic by also taking into account the weight, the age, the kind of
job, as well as the usual alimentation of the patient. The doctors cannot reason by
only taking into account the amount of glucose in blood, and under the schemes
of boolean reasoning. Once the current medical concepts are translated into fuzzy
terms it is necessary to follow the reasoning under those schemes of fuzzy logic
allowed in a suitably algebra of fuzzy sets designed accordingly with the context in
which the concepts are inscribed.
In addition, since the processes conducting to diagnose try to find a good enough
hypothesis, matching with the symptoms of the presumed illness, it is relevant for
the researchers on medical reasoning to know what is concerned with abduction
and speculation in both classical and fuzzy logic. It could be of some interest for
those researchers to know something on the more general framework considering
reasoning as the pair conjecturing + refuting) (see [5], [7], and [6]).
With all that, the authors are only trying to rescue the Sorites argument from the
kingdom of classical logic, where only boolean tautological reasonings are allowed,
and to place it into a total different kingdom where rational conjecturing based on
either experience, or experiments, is pertinent for obtaining mathematical models
with which knowledge can be controlled to progressively become deep and deep.
This is in fact, in the line of Zadeh's Computing with Words [10] or, at least, the
way the authors see it.
To some extent, to analyze Sorites' type problems with only strictly theoretic
boolean reasoning, is close to analyze the universe without using the telescope and
going back to times without the work of Kepler, Copernicus and Galileo.
Acknowledgement.
The authors warmly thank Prof. Claudio Moraga (ECSC), for his help
during the writing of this paper. This work has been supported by the Foundation for the
Advancement of Soft Computing (ECSC) (Asturias, Spain), and by the Spanish Department
of Science and Innovation (MICINN) under project TIN2008-06890-C02-01.
References
1. Black, M.: Reasoning with Loose Concepts. Dialogue 2, 1-12 (1963)
2. Masquelet, A.C.: Le Raisonnement Médical. PUF, Paris (2006) (in French)
3. Sorensen, R.A.: Vagueness and Contradiction. Clarendon Press, Oxford (2001)
4. Trillas, E.: On Negation Functions in Fuzzy Set Theory. In: Barro, S., Bugarin, A.,
Sobrino, A. (eds.) Advances of Fuzzy Logic, pp. 31-43. Universidad de Santiago de
Compostela (1998)
5. Trillas, E.: Conjectures in De Morgan Algebras and with Fuzzy Sets. Submitted to
NAFIPS 2012 (2012)
6. García-Honrado, I., Trillas, E.: On an Attempt to Formalize Guessing. In: Seising, R.,
Sanz González, V. (eds.) Soft Computing in Humanities and Social Sciences. STUD-
FUZZ, vol. 273, pp. 243-264. Springer, Heidelberg (2012)
