Imprecise data handling with MTE

Abstract

Measurements, indications and forecasts are randomly and very often systematically corrupted. The distribution of stochastic distortions is empirically evaluated; an estimate is usually given by histogram. Empirical distributions available from various sources differ. Discrepancies are due to testing methodology, conditions of experiments etc. Whatever the reason they introduce some kind of doubtfulness. In many modern applications propagation of uncertainty is an important issue. The ability to model and process uncertainty through traditional approaches is rather limited. To propose new solutions, one should start with an alternative approach towards modelling and processing uncertainty. Mathematical Theory of Evidence might be useful provided supporting measures on representing the true value by any location in the neighborhood of observation are available. Theoretical Gaussian density distribution as well as histograms are exploited. In recent paper by the author transformation from probability density to probability distribution with fuzzy sets was presented. In order to obtain most probable forecast various height histogram bins are converted to fuzzy limited ones. Necessary membership functions are proposed. Paper concludes with example calculations results.