The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances
If a possibility distribution and a probability distribution
are describing values x of one and the same system or process
x(t), can they relate to each other? Though in general the possibility
and probability distributions might be not connected at all, we
can assume that in some particular cases there is an association linked
them.
In the presented paper, we consider distributions of bloodstream
concentrations of physiologically active substances and propose that
the probability to observe a concentration x of a substance X can be
produced from the possibility of the event X = x .
The proposed assumptions and resulted theoretical distributions
are tested against the data obtained from various panel studies of the
bloodstream concentrations of the different physiologically active
substances in patients and healthy adults as well.
[1] Akay, M., Cohen, M., Hudson, D. Fuzzy sets in life sciences. Fuzzy Sets
and Systems, 90, 1997, pp. 219-224.
[2] Bilenko N, Yehiel M, Inbar Y, Gazala E. The association between
anemia in infants, and maternal knowledge and adherence to iron
supplementation in southern Israel. The Israel Medical Association
journal : IMAJ, 2007, 9(7), pp. 521-524.
[3] Bilenko, N., Shahar, D.; Shai, I.; Weitzman, S.; Fraser, D. Prevalence
and characteristics of myocardial infarction, dia-betes and hypertension
in the adult Jewish population: re-sults from the Negev Nutritional
Study. Harefuah, 142(1), 2003, pp. 17-21.
[4] Bolotin, A. The Possibility Distribution for the Controlled Bloodstream
Concentrations of Any Physiologically Active Substance. PWASET
Vol. 23, 2007, ISSN 1307-6884, pp. 61-66.
[5] Dubois, D. and Prade, H. Fuzzy sets in approximate reason-ing, Part 1:
Inference with possibility distributions. Fuzzy Sets and Systems, Vol.
40, 1991, pp. 143-202.
[6] Fraser D, Bilenko N, Vardy H, Abu-Saad K, Shai I, Abu-Shareb H,
Shahar DR. Differences in food intake and dispar-ity in obesity rates
between adult Jews and Bedouins in southern Israel. Ethnicity &
disease, 2008, 18(1), pp. 13-18.
[7] Mathews, C. K. and Holde, K. E. Integration and control of metabolic
processes. In: D. Bowen. Biochemistry. s.l. : Ben-jamin/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 In-stitutes of Health,
Date last updated: 26 February 2009. [Cited: December 11, 2009.]
http://www.nlm.nih.gov/medlineplus/encyclopedia.html.
[9] Nguyen, H.T. Fuzzy sets and probability. Fuzzy Sets and Systems, 90,
1997, pp. 129-132.
[10] Rouvray, D. H. The treatment of uncertainty in the sciences. Endeavour,
Vol. 21 (4), 1997, pp.154-158.
[11] Spott, M. A theory of possibility distributions. Fuzzy Sets and Systems,
Vol. 102, 1999, pp. 135-155.
[12] Zadeh, L. A. Toward a perception-based theory of probabil-istic
reasoning. Journal of Statistical Planning and Inference, 105, 2002, pp.
233-264.
[1] Akay, M., Cohen, M., Hudson, D. Fuzzy sets in life sciences. Fuzzy Sets
and Systems, 90, 1997, pp. 219-224.
[2] Bilenko N, Yehiel M, Inbar Y, Gazala E. The association between
anemia in infants, and maternal knowledge and adherence to iron
supplementation in southern Israel. The Israel Medical Association
journal : IMAJ, 2007, 9(7), pp. 521-524.
[3] Bilenko, N., Shahar, D.; Shai, I.; Weitzman, S.; Fraser, D. Prevalence
and characteristics of myocardial infarction, dia-betes and hypertension
in the adult Jewish population: re-sults from the Negev Nutritional
Study. Harefuah, 142(1), 2003, pp. 17-21.
[4] Bolotin, A. The Possibility Distribution for the Controlled Bloodstream
Concentrations of Any Physiologically Active Substance. PWASET
Vol. 23, 2007, ISSN 1307-6884, pp. 61-66.
[5] Dubois, D. and Prade, H. Fuzzy sets in approximate reason-ing, Part 1:
Inference with possibility distributions. Fuzzy Sets and Systems, Vol.
40, 1991, pp. 143-202.
[6] Fraser D, Bilenko N, Vardy H, Abu-Saad K, Shai I, Abu-Shareb H,
Shahar DR. Differences in food intake and dispar-ity in obesity rates
between adult Jews and Bedouins in southern Israel. Ethnicity &
disease, 2008, 18(1), pp. 13-18.
[7] Mathews, C. K. and Holde, K. E. Integration and control of metabolic
processes. In: D. Bowen. Biochemistry. s.l. : Ben-jamin/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 In-stitutes of Health,
Date last updated: 26 February 2009. [Cited: December 11, 2009.]
http://www.nlm.nih.gov/medlineplus/encyclopedia.html.
[9] Nguyen, H.T. Fuzzy sets and probability. Fuzzy Sets and Systems, 90,
1997, pp. 129-132.
[10] Rouvray, D. H. The treatment of uncertainty in the sciences. Endeavour,
Vol. 21 (4), 1997, pp.154-158.
[11] Spott, M. A theory of possibility distributions. Fuzzy Sets and Systems,
Vol. 102, 1999, pp. 135-155.
[12] Zadeh, L. A. Toward a perception-based theory of probabil-istic
reasoning. Journal of Statistical Planning and Inference, 105, 2002, pp.
233-264.
@article{"International Journal of Medical, Medicine and Health Sciences:51930", author = "Arkady Bolotin", title = "The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances", abstract = "If a possibility distribution and a probability distribution
are describing values x of one and the same system or process
x(t), can they relate to each other? Though in general the possibility
and probability distributions might be not connected at all, we
can assume that in some particular cases there is an association linked
them.
In the presented paper, we consider distributions of bloodstream
concentrations of physiologically active substances and propose that
the probability to observe a concentration x of a substance X can be
produced from the possibility of the event X = x .
The proposed assumptions and resulted theoretical distributions
are tested against the data obtained from various panel studies of the
bloodstream concentrations of the different physiologically active
substances in patients and healthy adults as well.", keywords = "Possibility distributions, possibility-probability relationship.", volume = "3", number = "9", pages = "220-8", }