| With the development of Artificial Intelligence with uncertainty, Granular Computing imprecise probability and its graphical models have been focus on the region of approximate modeling and reasoning in Artificial Intelligence. After an overview on the research over the world, the some basic theories and applications of them in this thesis are investigated as follows:1. Quotient space approachability theory basing on measure spaces is put forward with respect to Quotient Space theory that is one of the main model in Granular Computing, as the same time, a semi-order structure fusion method under the condition of inconsistency information is presented.2. Causal qualitative networks (namely, Qualitative probabilistic networks (abbriv. QPNs), or qualitative Bayesian networks) are qualitative abstractions of Bayesian networks, bearing a strong resemblance to their quantitative counterparts, and are a graphical model for imprecise probability; Credal networks, as a representation for a set of Bayesian networks over a fixed set of variables, is another graphical model for imprecise probability. In factual applications, different part information of Bayesian networks can be obtained for some problem so that integrating them into a whole is necessary. Basing on the above, a new concept, namely generalized causal qualitative networks, is presented; as the same time its qualitative fusion method is put forward due to Granular Computing.3. Constructive learning methods based on covering has advantages for handling huge amount multiclass and high dimensionality data according to training samples, but its some defects such as samples of refused-recognition appear. In the thesis, a new algorithm named causal covering algorithm is presented through associating causal networks with constructive learning with respect to computing learning theory. Causal covering algorithm provides a new method for improvement of the covering algorithm because of harnessing causal information in training samples.
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