A fuzzy approach to the definition of standardized visibility in fog.

The problem of defining the physical concept of standardized visibility is addressed by means of a fuzzy logic approach. Assuming that several hypotheses hold, it is possible to evaluate a standardized visibility Vk (or meteorological visual range) as the ratio of a psychometric coefficient k and the extinction coefficient σ of the aerosol. The main disadvantage of this relationship due to Koschmieder stems from the fact that the meteorological visual range can be very different from visibility estimated by a human observer with normal sight. This is particularly true during fog extinction coefficient supplied by a transmissometer and the corresponding visibility evaluated by an expert. Calculations are performed according to two different approaches. First, a so-called fuzzy hyperbolic model based on a distance defined by Bardossy et al is presented, yielding a crisp (nonfuzzy) value of the coefficient k. Next, we use the multiplication of two fuzzy numbers, taken as triangular, to build an average fuzzy number k that accounts for the different values found in the literature. The defuzzification of k confirms the result obtained by the first approach.