Fuzzy indices of risk for a deeper evaluation of exposure-affection studies

Maurizio Brizzi


In this paper a fuzzy version of three indices of risk (Diagonal Ratio, Rate ratio and Odds ratio), usually applied to exposure-affection studies, has been proposed and developed, considering the presence of a partial level of exposure and/or affection. These fuzzy indices are calculated after rescaling the cell frequencies according to fuzzy degrees of pertinence of partial modalities.
A simulation study has then been performed, under the hypothesis of absence of effect of the risk factor, and some exploratory statistics have been reported, corresponding to different sample sizes; a transformed linear interpolation method has been described for extending simulation results. The rescaling method has been generalized, supposing that every observation has its proper level of exposure and affection. Finally, the fuzzy indices have been applied to an Italian survey, dealing with the relationship between physical activity and self-perceived health status of more than 4,500 people over 65, living in the province of Bologna.


Exposure-affection study; Indices of risk; Diagonal ratio, Fuzzy logic; Monte Carlo simulation

Full Text:

PDF (English)


A. AGRESTI (2007). An introduction to categorical data analysis. Chapter 2. John Wiley & Sons, New York.

B. F. ARNOLD (1996). An approach to fuzzy hypothesis testing. Metrika, 44, pp. 119{126.

M. BRIZZI (2002). The relationship between the relevance quotient and the indices of risk in a 2x2 exposure-affection table. Methodology and Statistics, Ljubljana 2002, pp. 25{28.

M. BRIZZI (2004). Indices of risk based on relevance quotients, with an application to self-assessed health status. Atti della XLII Riunione Scientica SIS, Bari. Contributi spontanei, pp. 345{348.

S. BROCCOLI, G. CAVRINI, M. ZOLI (2005). Il modello di regressione quantile nell’analisi delle determinanti della qualit di vita in una popolazione anziana. Statistica, LXV, 4, pp. 419{436.

J. J. BUCKLEY (2005). Fuzzy statistics: hypothesis testing. Soft Computing, 9, pp. 512{518

G. CAVRINI, B. PACELLI, A. MATTIVI, G. BIANCHI, P. PANDOLFI, M. ZOLI (2005). Benets of physical activities on the perceived health in elderly people. Proceedings of the 7th European Meeting of EuroQol, Oslo.

A. COLUBI (2009). Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data. Fuzzy sets and systems, 160, pp. 344{356.

R. M. COOKE (1991). Experts in uncertainty. Opinion and subjective probability in science. Oxford University Press.

A. FALSAFAIN, S. M. TAHERI, M. MASHINCHI (2008). Fuzzy estimation of parameters in statistical models. International Journal of Computational and Mathematical Science, 2, pp. 79-85.

A. FALSAFAIN, S. M. TAHERI (2011). On Buckleys approach to fuzzy estimation. Soft Computing, 15, pp. 345-349.

S. FRHWIRTH-SCHNATTER (1992). On statistical inference for fuzzy data with applications to descriptive statistics. Fuzzy sets and systems, 50, pp. 143-165.

R. KRNER (2000). An asymptotic test for the expectation of fuzzy random variables. Journal of Statistical Planning and Inference, 83, pp. 331-346.

T. RUDAS (1998). Odds Ratios in the Analysis of Contingency Tables. SAGE Publishing Editor.

S. M. TAHERI (2003). Trends in fuzzy statistics. Austrian Journal of Statistics, 32, pp. 239{257.

R. VIERTL (2011). Statistical methods for fuzzy data. John Wiley & Sons, New York.

L. A. ZADEH (1995). Probability theory and fuzzy logic are complementary rather than competitive. Technometrics, 37, pp. 271{277.

DOI: 10.6092/issn.1973-2201/6682

Creative Commons License 

ISSN 1973-2201

Registration at Bologna Court Law no. 2476 on 24th February 1955 (in progress)

The journal is hosted and mantained by ASDD-AlmaDL [privacy]