On the influence of data noise and uncertainty on ordering of objects, described by a multi-indicator system. A set of pesticides as an exemplary case

摘要

A priori in partial ordering methodology the input data are understood as exact and true values, which is denoted as the "original data matrix". As such even minor differences between values are regarded as real. However, in real life data are typically associated with a certain portion of noise or uncertainty. Hence, introducing noise may cause changes in the overall ordering of objects. The present paper deals with the effects of data noise or uncertainties on the partial ordering of a series of objects, a series of obsolete pesticides being used as an illustrative example. The approach is fuzzy like, and partially ordered sets are obtained as function of noise. A main focus of the work is to identify the range in terms of noise, where the original partial order is retained. We call this range the "stability range". It is demonstrated that by increasing data noise the range where the "original partial order" is obtained decreases. The original partial order is based on the original data matrix. Further, it is found that significant changes in the partial ordering appear outside of this stability range. The possible relation between data noise and the stability range is discussed on an empirical basis. Copyright (C) 2015 John Wiley & Sons, Ltd.