The aim of this article is to illustrate a procedure for applying the precautionary principle within a strategy for reducing the possibility of underestimating the effective risk caused by a phenomenon, product, or process, and of adopting insufficient risk reduction measures or overlooking their need. We start by simply defining risk as the product between the numerical expression of the adverse consequences of an event and the likelihood of its occurrence or the likelihood that such consequences will occur. Uncertainty in likelihood estimates and several key concepts inherent to the precautionary principle, such as sufficient certainty, prevention, and desired level of protection, are represented as fuzzy sets. The strategy described may be viewed as a simplified example of a precautionary decision process that has been chiefly conceived as a theoretical contribution to the debate concerning the precautionary principle, the quantification of its application, and the formal approach to such problems.

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The paper illustrates an approach for implementing the Precautionary Principle in risk management, exemplified by a procedure aimed at choosing the height of a rockfall barrier protecting a railway stretch. Risk is expressed by the frequency f of blocks hitting the railway-i.e. by the ratio between the number of blocks reaching the railway and the number of blocks falling from the slope-assessed through software simulation of the falling of the blocks. The height from which a block may fall is considered to be the main uncertainty factor in risk estimation, which translates into uncertainty as to the level of risk, as every simulation shows that more than one impact frequency is possible. Such uncertainty justifies the precautionary approach to the design of the barrier, and is represented mathematically by means of possibility and probability distribution functions. The distributions make it possible to express the degree of precaution related to a barrier as the level of confidence, in terms of necessity or probability measures-that can be placed on the fact that, because of the barrier, the impact frequency, although uncertain, will not exceed what is acceptable. It will be shown that the degree of precaution takes quite different values if possibility theory is used instead of probability theory. Finally some simple cost/ benefit analyses, that explicitly and quantitatively consider the degree of precaution, are exemplified.

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