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Given a data set how to assign definitions to the subsets. For instance given the data

data = {{0, 1, 1}, {0, 1, 1}, {1, 1, 0}, {0, 1, 1}, {1, 1, 0}}

if {0, 1, 1} is SetA and {1, 1, 0} is SetB the result would be data={SetA, SetA, SetA, SetB, SetA}

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You can use ReplaceAll:

rules = {{0, 1, 1} -> setA, {1, 1, 0} -> setB};

data /. rules
{setA, setA, setB, setA, setB}

Alternatively, define a function that evaluates to setA for {0,1,1} and to setB for {1,1,0} and map it on data:

ClearAll[f]
f[{0, 1, 1}] = setA;
f[{1, 1, 0}] = setB;

f /@ data
{setA, setA, setB, setA, setB}
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