Topological Analysis on the Belief Rule Base Space

The belief rule base (BRB) uses the “IF-THEN” rule to handle different types of information under uncertainty, and then transforms them into a unified result in the same belief structure as the input. In this paper, the BRB space is analyzed from a new topological perspective, based on which three conclusions are derived: 1) the BRB space is an attribute product measure space; 2) a rule in BRB is a vector in the BRB space and the rule integration process by any input is a vector calculation process, and 3) the vector calculation follows from the commutative and associative laws of addition while the dot product of the vectors reflects their distance in the BRB space. An illustrative example is given to better clarify the proposed topological analysis on the BRB space. The limitations and future work are investigated as a conclusion.