Effects of scale on longitudinal dispersivity are often determined using regression correlations developed from compiled dispersivity data in most risk and remedial applications. However, only 75% of the observed variation is explained by statistical regression equations and existing stochastic theories. As such, the available dispersivity data are considered to be imprecise (in a non-statistical sense) in this study, and fuzzy least-squares regression methodology has been utilized to develop scale-dispersivity relationships. An attempt has also been made to include the reliability of the available data into the fuzzy regression scheme. Fuzzy regression models have been developed for log-transformed and log-log-transformed scale data. The results indicate that fuzzy regression is able to capture the imprecision in the observed data better than statistical models. However, this superiority of the fuzzy regression was observed to decrease with increasing strength of scale-dispersivity correlation obtained by log-log linearization of the scale data.
- Fuzzy sets
- Parameter estimation