# Sustainability

According to Figure 10, there are 25 selected studies that present their approaches at the three abstraction levels and eight studies at two levels differentiated from logical to physical, conceptual to logical and conceptual to physical. According to this concept, the proposed approaches for the transformation between the data abstraction levels are presented.

As presented in Figure 14, there are 19 studies where the authors propose their own novel mapping rules, which demonstrates the separate research that exists on this topic. Thus, it is difficult to decide which is the most appropriate when selecting any of them. Another interesting aspect is that 12 studies do not define transformation rules and there are six studies that propose transformations based on other techniques, such as the Linearization Algorithm (LA), ATL Transformation Language (ATL), Hoberman Heuristic (HH), Algorithm Cardinality (AC), Category Theory (CT) and Workload Space Constraint (WSC).

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Sustainability 2019, 11, x FOR PEER REVIEW

Transformation Language (ATL), Hoberman Heuristic (HH), Algorithm Cardinality (AC), Category Theory (CT) and Workload Space Constraint (WSC).

Figure 14. Transformation between data abstraction levels.

In general, the authors propose the below algorithm that takes a model as input, apply their own transformation rules and produce another model as output:

Input1: Conceptual Level: πΆ πΆ , where πΆ belongs to each π element from conceptual model. Transformation rules: π π , where π belongs to each π rule or constraint from mapping rules defined by the authors. Output1: Logical Level: πΏ πΆ βͺ π π , where π belongs to each π element from logical model. Input2 = Output 1 Transformation rulesβ: πβ² πβ² , where πβ² belongs to each π rule or constraint from mapping rules defined by the authors. Output2: Physical Level: π πΏ βͺ π π , where π belongs to each π element from physical model.

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