We develop new methods for the representation of uncertainty in the granularized information source values by making use of the entropy framework in the possibilistic domain. An information-theoretic entropy function is used to map the information source values to information (entropy) values. We term a collection of such information values as an information set. The information values are then used in an adaptive form of this entropy function to formulate Shannon transforms. A few uncertainty measures are derived from these transforms for the quantification of uncertainty. Information set is also extended to other domains, such as probabilistic, intuitionistic, and probabilistic-intuitionistic domains. A biometric application is included to demonstrate the usefulness of the study. © 1993-2012 IEEE.