Appendix B: The Fuzzy Set Theory (original) (raw)

The uncertainty inherent in data, values of parameters, boundary conditions or variables used as inputs to mathematical models may be quantified by use of stochastic variables. As an example, let us consider the mortality of bacteria, which may be considered as a parameter useful to characterise the quality of a water sample. If the mortality has large values, then bacteria are eliminated and the water quality has a good chance of remaining acceptable. Mortality of bacteria is influenced by several factors, such as temperature, solar light, salinity and some biological characteristics. Usually, all these parameters are taken into consideration by means of the characteristic time t 90 , that is the time necessary to eliminate 90% of bacteria. Because of the various uncertainties, t 90 may be considered to be a random variable having a probability density distribution. As shown in .1, a log-normal probability density function may be used to fit the available data and represent uncertainties in the values of t 90 .