Quotient space approachability basing on measure space and fusion model of weighted graphical structure

In this paper, a fusion model of weighted semi-order spaces is presented as well as the quotient space approachability theorem basing on measure space is proved. Fusion theory is not only concerned with information fusion, but with space structure that topology relation among elements on the space exists. We consider inductive reasoning basing on granularity analysis is also a kind of fusion in light of the quotient space approachability theorem. While qualitative thing is uncertain to the corresponding quantitative thing basing on the theory of quotient space, the theory in the paper can be used to integrate qualitative probabilistic networks, as qualitative analogues to an original Bayesian networks, abstracting from the numerical detail.