Fuzzy regression in hydrology

Abstract

A general methodology for fuzzy regression is developed and illustrated by an actual hydrological case study. Fuzzy regression may be used whenever a relationship between variables is imprecise and/or data are inaccurate and/or sample sizes are insufficient. In such cases fuzzy regression may be used as a complement or an alternative to statistical regression analysis. In fuzzy regression, several “goodness of fit” criteria may be used such as the maximum average vagueness criterion and the prediction vagueness criterion. The technique is illustrated by means of a case study involving the relationship between soil electrical resistivity and hydraulic permeability. This relationship is imprecise and based on only a few data points. In the present case a curvilinear relationship is fitted using fuzzy regression with six calculated resistivities and six measured permeabilities. Prediction vagueness criteria appears to yield a more robust fuzzy regression than the maximum average vagueness criteria. Potential application areas of fuzzy regression in hydrology are discussed further. The methodology is relatively simple, and the results can be interpreted to provide a valuable hydrological decision‐making aid.