A multi-granular computing architecture

namely a top-down decomposition and bottom-up synthesis is proposed.The structure plays a very important role in quotient space model(QSM)

and the QSMs with different structures generally vary.With respect to composition

a composition of topologies of different quotient spaces is generally not a quotient topology

while a operator composition of operators of different quotient spaces is a quotient operator.As for decomposition

it acquires the two important conclusions when defining the concepts of problem equivalence and reversible decomposition.One is that the granulation for two structures by means of either chained or directed are equivalent

the other is that an orthogonal decomposition in QSM with a algebraic structure is reversible

but a similar conclusions is not true in QSM with a topological structure.