Representation of Uncertainty with Information and Probabilistic Information Granules

Linguistic representations by human brain are often characterized with an intertwined combination of imprecision (due to incomplete knowledge), vagueness, or uncertainty. A powerful framework of information and probabilistic information granules is proposed to model this combination of different facets of uncertainty in natural representations without distortion of the underlying meaning. The proposed notions are deployed in formulation of a comprehensive approach to model complex uncertain situations involving imprecise/inexact probabilities of fuzzy events. The concepts are based upon the principle of information granulation that can be viewed as a human way of achieving data compression. The proposed approach closely resembles the implementation of the strategy of divide-and-conquer which brings it close to human problem-solving thought process. The study also makes an attempt to minimize distortion of information in its representation by fuzzy logic.