This issue of the International Journal of Intelligent Systems presents approaches to knowledge discovery based on rough set theory. [1][2][3][4][5][6][7][8] It is often the case that there are imperfections in raw input data needed for knowledge acquisition: uncertainty, vagueness, and incompleteness. Uncertainty arises in any measuring process where the observed value of a variable x tends to fluctuate from one measurement to the next. 9 Sensors have varying accuracy. Sensor readings can fluctuate and can sometimes be inaccurate due to noisy environments or faulty sensor components. Hence, there is keen interest in having measures of uncertainty. In the context of data mining and knowledge discovery, there is interest in quantifying the certainty factor of a decision rule. 2 In rough set theory, every decision rule has two conditional probabilities associated with it: certainty and coverage factors. 8 These two factors are closely related to two fundamental concepts of rough set theory, namely, lower approximation and upper approximation. It has been shown that the certainty and coverage factors satisfy Bayes' rule. 8 In addition, a frequency-based estimate of the conditional probability that an object x belongs to a set X has also been introduced in rough set theory 4 (see also Ref. 3). Other rough set approaches to measurement in the presence of uncertainty have also been given (see for example Refs. 3 and 6). Vagueness is yet another nettlesome problem in data mining and knowledge discovery. Two common sources of vagueness have been identified: error in physical measurements due to inaccurate measuring devices, as well as the mixture of noise and pure signals