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Within the context of Data Warehouse(DW), I would like to know:
Why is it correct to state that this approach (Bottom Up) does not guarantee standardization of metadata, and may create data inconsistencies between Data Marts (DM).
I found an article interesting to explain how the two approaches works Top Down and Bottom Up. But it does not explain the above statement.
The above statement is template of a test question.
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On the Internet I was able to find this justification:
The author of the book states:
Kimball’s proposed Botton Up architecture, called "Bottom Up", begins with the extraction, transformation, and integration of data into one or more Dms, these Dms being modeled, usually through a dimensional model. It presents as positive points, the rapid implementation; the agility in the presentation of results and the possibility of emphasizing first the main sectors of the business. The main disadvantage found is the lack of standardization of data Mart’s that can lead to redundancy and inconsistent data. (MACHADO, 2004).
The above statement made more sense after reading of that Article which explains:
The article states:
Data Marts are created in a autonomous and independent of the other Data Mart, that is, each one does as they see fit, and certainly this justifies the lack of standardization.
Case the word inconsistency be interpreted as redundancy of records, then it is possible to state that the lack of standardization generates inconsistency.
However, it does not justify the inconsistency of data in DW, due to ETL(Extraction, Transformation and load(load)), cited by the axe author.
An illustration representing the approach (Bottom Up) 
Corrected image of this source
That’s the answer to your question?
Well, then it would be more interesting to be an issue of the question, not an answer. Unless you accept it as a solution, even incomplete.
OK, I will accept the answer after 2 days, it was the message you gave here, when I tried to accept the answer.
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In this question https://www.gabarite.com.br/questoes-de-concursos/642571-questao related to the subject the answer is data Mining.
– Rod