Constructing Three-Way Decision With Fuzzy Granular-Ball Rough Sets Based on Uncertainty Invariance

Abstract

Granular-ball computing (GBC) proposed by Xia adaptively generates a different neighborhood for each object, resulting in greater generality and flexibility. Moreover, GBC greatly improves the efficiency by replacing point input with granular-ball. However, the current GB-based classifiers rigidly assign a specific class label to each data instance and lacks of the necessary strategies to address uncertain instances. These far-fetched certain classification approachs toward uncertain instances may suffer considerable risks. In this article, we introduce three-way decision (3WD) into GBC to construct a novel three-way decision with fuzzy granular-ball rough sets (3WD-FGBRS) from the perspective of uncertainty. This helps to construct reasonable multigranularity spaces for handling complex decision problems with uncertainty. First, 3WD-FGBRS is constructed in a data-driven method based on fuzziness, which avoids the subjective definition of certain risk parameters when calculating the threshold pairs. Based on 3WD-FGBRS, we further propose a sequential three-way decision with fuzzy granular-ball rough sets (S3WD-FGBRS) and analyze the fuzziness loss of multilevel decision result in S3WD-FGBRS. Then, the optimal granular-ball space selection mechanism of S3WD-FGBRS is introduced by combining fuzziness and granular-ball space distance. Finally, extensive comparative experiments are conducted with 3 state-of-the-art GB-based classifiers and 3 classical machine learning classifiers on 12 public benchmark datasets. The results show that our models almost outperform other comparison methods in terms of effectiveness, efficiency and robustness.