An Attempt to Understand Noisy Posets

The role of data noise is analyzed for a pair of objects and m indicators (m > 1) with respect to order relations. A general probability scheme is developed and by specifying a noise-model and a distribution for noisy values explicit expressions are derived. These expressions allow an a priori estimation at which noise level effects the order relation between the two objects are affected. It turns out that a useful quantity can be introduced, by which it can be decided at which level of noise perturbations on the set of order relations can be expected. We call this quantity the "crucial noise". Some toy examples and an example out of environmental chemistry are discussed.