| In hydrology and water resources management problems the theoretical probability distribution functions are widely used with the aim of the empirical probability function. However, it is difficult to exploit the probability functions in case that algebraic operations between random variables are required. A solution should be the motivation from the probability functions to fuzzy sets by using the fuzzy estimators. Finally based on the possibility theory the authors conclude that based on a probability distribution, a possibility distribution with the maximum specificity can be produced, that is near to the probability measure. The Reconnaissance Drought Index (RDI) was proposed to assess meteorological drought severity based on the precipitation to potential evapotranspiration ratio (P/PET). However it is difficult to express the bivariate probability density function for this ratio. Hence based on the fuzzy estimators, the analysis can be concluded to fuzzy sets, and the extension principle of fuzzy sets can provide the required ratio as fuzzy sets. |
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