Where does rough collide?

In computer science and mathematics, a rough set is a way of approximating a set whose membership is uncertain because objects can be told apart only up to some indiscernibility relation: it is represented by a lower approximation (objects surely in the set) and an upper approximation (objects possibly in it), the gap between them being the boundary region. Pawlak's 1982 Rough sets introduced the theory, now used in data analysis, feature selection, and reasoning about incomplete information. The referent is a pair of approximations bounding an imprecise concept, with no connection to uncut grass or a machined finish beyond the word.[1]

Unit

A set approximated by lower and upper bounds under an indiscernibility relation

Recovery means

Not applicable

Measured by

Characterised by the size of the boundary region and the accuracy of approximation

In surface metrology, roughness is the fine-scale irregularity of a surface (the closely spaced peaks and valleys left by machining or finishing), separated from the larger-scale waviness and overall form of the part. Whitehouse's Handbook of Surface and Nanometrology sets out how these deviations are filtered and quantified by parameters such as the arithmetic mean deviation Ra. The referent is the micro-texture of a solid surface, measured in micrometres, and it shares only the word with a golf-course zone or a rough set.[2]

Unit

The fine-scale height deviation of a surface, in micrometres

Recovery means

Not applicable

Measured by

Quantified by texture parameters such as Ra and Rz after filtering out waviness and form