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

#### Abstract

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.

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DOI: 10.6092/issn.1973-2201/6682