The Possibility Distribution for the Controlled Bloodstream Concentrations of Any Physiologically Active Substance

In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, there are hardly any applications of possibility theory in biology or medicine. The aim of this work is to demonstrate the use of possibility theory in an epidemiological study. In the paper, we build the possibility distribution for the controlled bloodstream concentrations of any physiologically active substance through few approximate considerations. This possibility distribution is tested later against the empirical histograms obtained from the panel study of the eight different physiologically active substances in 417 individuals.

• Arkady Bolotin

• Possibility distributions
• physiologically activesubstances
• bloodstream concentrations.

[1] Bilenko, N., Shahar, D.; Shai, I.; Weitzman, S.; Fraser, D. Prevalence
and characteristics of myocardial infarction, diabetes and hypertension
in the adult Jewish population: results from the Negev Nutritional Study.
Harefuah, 142(1), 2003, pp. 17-21.
[2] Dubois, D. and Prade, H. Fuzzy sets in approximate reasoning, Part 1:
Inference with possibility distributions. Fuzzy Sets and Systems, Vol.
40, 1991, pp. 143-202.
[3] Dubois, D. and Prade, H. Bayesian conditioning in possibility theory.
Fuzzy Sets and Systems , Vol. 92, 1997, pp. 223-240.
[4] G. Klir (2000). On fuzzy-set interpretation of possibility theory. Fuzzy
sets and systems, Vol. 108, 2000, pp. 263-273.
[5] Inuiguchi, M.; Tanino, T.; Sakawa, M. Membership function elicitation
in possibilistic programming problems. Fuzzy Sets and Systems, Vol.
111, 2000, pp. 29-45.
[6] Janssen, Hugo, de Cooman, Gert and Kerre, Etienne E. A Daniell-
Kolrnogorov theorem for supremum preserving upper probabilities.
Fuzzy Sets and Systems, Vol. 102, 1999, pp. 429-444.
[7] Mathews, C. K. and Holde, K. E. Integration and control of metabolic
processes. In: D. Bowen. Biochemistry. s.l.: Benjamin/Cummings
Publishing Group, 1990, pp. 790-792.
[8] Medical Encyclopedia. Medline Plus. (Online) A service of the U.S.
National Labrary of Medicine and the National Institutes of Health, May
2, 2007. (Cited: May 16, 2007.)
http://www.nlm.nih.gov/medlineplus/encyclopedia.html.
[9] Spott, Martin. A theory of possibility distributions. Fuzzy Sets and
Systems, Vol. 102, 1999, pp. 135-155.
[10] Zadeh, L.A. Fuzzy sets as a basis for a theory of possibility Fuzzy Sets
and Systems, Vol. 1, 1978, pp. 3-28.