A fuzzy approach to the definition of standardized visibility in fog

摘要

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 [7] 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 occurrences. A fuzzy approach is used to evaluate a relationship between the 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 [2] 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 k̃ that accounts for the different values found in the literature. The defuzzification of k̃ confirms the result obtained by the first approach.