Decomposition Into Granules Speeds Up Data Processing Under Uncertainty

In many real-life situations, uncertainty can be naturally described as a combination of several components, components which are described by probabilistic, fuzzy, interval, etc. granules. In such situations, to process this uncertainty, it is often beneficial to take this granularity into account by processing these granules separately and then combining the results. In this paper, we show that granular computing can help even in situations when there is no such natural decomposition into granules: namely, we can often speed up processing of uncertainty if we first (artificially) decompose the original uncertainty into appropriate granules. 1 Need to Speed Up Data Processing Under Uncertainty: Formulation of the Problem Need for data processing. One of the main reasons for data processing is that we are interested in a quantity y which is difficult (or even impossible) to measure or estimate directly. For example, y can be a future value of a quantity of interest. To estimate this value y, we: • find easier-to-measure and/or or easier-to-estimate quantities x1, . . . , xn which are related to y by a known dependence y = f(x1, . . . , xn), • measure or estimate xi’s, and • use the known relation y = f(x1, . . . , xn) to predict y. Need to take uncertainty into account. Due to measurement uncertainty, the measurement results x̃i are, in general, different from the actual values xi