Glossary

This page defines the main execution and fuzzy-rough terms used in FRsutils. Definitions are intentionally short so they can be used consistently across the README, user documentation, benchmark reports, and the software manuscript.

Dense execution

Execution mode that builds or uses the full pairwise similarity matrix in memory. In FRsutils, the standard dense path uses NumPy.

Blockwise execution

Execution mode that computes exact fuzzy-rough results by processing similarity blocks instead of materializing the full similarity matrix. Blockwise execution reduces pairwise-computation memory use; it does not currently provide disk-backed or streaming dataset loading, so the input feature matrix X is expected to fit in memory.

Backend

The array/computation library used internally for supported operations. The stable default backend is NumPy. CuPy is optional and currently limited to selected backend-aware paths.

Public output

The result returned by the public API. FRsutils returns public result arrays as NumPy arrays, even when CuPy is used internally.

GPU-backed similarity blocks

Similarity blocks computed with the CuPy backend during supported blockwise execution.

GPU-resident approximation accumulators

Model-specific intermediate approximation arrays that remain on the GPU during supported blockwise computation before final conversion to NumPy public output.

Engine

The high-level execution mode selected by the public API, usually "dense" or "blockwise".

Similarity matrix

A pairwise matrix where entry (i, j) stores the fuzzy similarity between sample i and sample j.

Lower approximation

The fuzzy-rough degree to which each sample certainly belongs to a target class or concept.

Upper approximation

The fuzzy-rough degree to which each sample possibly belongs to a target class or concept.

Signed boundary

The un-clipped difference between upper and lower approximation degrees: upper - lower. It can be negative when a model configuration does not guarantee that the upper approximation is at least the lower approximation. The older name boundary region remains available in the API for backward compatibility.

Positive region

A fuzzy-rough score summarizing how confidently samples can be associated with their decision class.