## Approximate entropy reducts.(English)Zbl 1092.68676

Summary: We use information entropy measure to extend the rough set based notion of a reduct. We introduce the Approximate Entropy Reduction Principle (AERP). It states that any simplification (reduction of attributes) in the decision model, which approximately preserves its conditional entropy (the measure of inconsistency of defining decision by conditional attributes) should be performed to decrease its prior entropy (the measure of the model’s complexity). We show NP-hardness of optimization tasks concerning application of various modifications of AERP to data analysis.

### MSC:

 68T37 Reasoning under uncertainty in the context of artificial intelligence 94A17 Measures of information, entropy