Adapting Fuzzy Rough Sets for Classification with Missing Values

Abstract

We propose an adaptation of fuzzy rough sets to model concepts in datasets with missing values. Upper and lower approximations are replaced by interval-valued fuzzy sets that express the uncertainty caused by incomplete information. Each of these interval-valued fuzzy sets is delineated by a pair of optimistic and pessimistic approximations. We show how this can be used to adapt Fuzzy Rough Nearest Neighbour (FRNN) classification to datasets with missing values. In a small experiment with real-world data, our proposal outperforms simple imputation with the mean and mode on datasets with a low missing value rate.

Decoding pan-cancer treatment outcomes using multimodal real-world data and explainable artificial intelligence

“…Missing values were set to (0,0). 42 This has been used previously in comparable biomedical settings. 43,44 Feature expansion was only applied to features that had missing values.…”

Presumably correct decision sets

“…In other words, by taking a specific set of nominal features, we create an equivalence class in which each instance is indiscernible from the others. The upper approximation is the union of all equivalence classes, which have a non-empty intersection with the set being approximated [22]. In the presence of numeric features, the equivalence classes are replaced by similarity classes, thus leading to a soft partition of the universe.…”