The idea that decompositions are tools from breaking down and thinking about complexity and vagueness is not foreign to most people. Structuring however is less though of, while still being just as common.
It is used every day, in a grant proposals, research reports, emails, and so on. In any situation where collected information is combined into an digestible or understandable format we are using structure to make sense of the complex.
In an analysis situation, when presented with abstract, vague, or complex information we need to structure that information in such a way as to enable understanding and context.
Modelling and diagramming are examples of structuring