A robust three-way classifier with shadowed granular-balls based on justifiable granularity

TL;DR

This work addresses the risk of misclassification in GB-based classifiers by introducing a robust three-way classifier that handles uncertainty via shadowed granular-balls and a three-way decision framework. It proposes an information-entropy driven GB generation method that balances coverage and specificity through the measure $L_{ ext{G}}$, and constructs shadowed GBs using an optimal threshold $(oldsymbol{ ightarrow},1-oldsymbol{ ightarrow})$ to create Core, Important, and Unessential regions. A set of decision rules based on controlled regions integrates fuzzy-rough transformations and 3WD to yield outputs as either certain class labels or uncertain cases, reducing risk in ambiguous samples. Extensive experiments on 12 public datasets across varying noise levels demonstrate improved robustness and competitive accuracy, with significant efficiency gains compared to GB-based methods. The approach offers a principled, scalable pathway for robust uncertain-data classification in granular-ball frameworks, with potential applicability to decision-support and CAD-like systems.

Abstract

The granular-ball (GB)-based classifier introduced by Xia, exhibits adaptability in creating coarse-grained information granules for input, thereby enhancing its generality and flexibility. Nevertheless, 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. To solve this problem, we construct a robust three-way classifier with shadowed GBs for uncertain data. Firstly, combine with information entropy, we propose an enhanced GB generation method with the principle of justifiable granularity. Subsequently, based on minimum uncertainty, a shadowed mapping is utilized to partition a GB into Core region, Important region and Unessential region. Based on the constructed shadowed GBs, we establish a three-way classifier to categorize data instances into certain classes and uncertain case. Finally, extensive comparative experiments are conducted with 2 three-way classifiers, 3 state-of-the-art GB-based classifiers, and 3 classical machine learning classifiers on 12 public benchmark datasets. The results show that our model demonstrates robustness in managing uncertain data and effectively mitigates classification risks. Furthermore, our model almost outperforms the other comparison methods in both effectiveness and efficiency.

Figures (8)

• Figure 1: The GB generation with purity when facing noise
• Figure 2: Transformation from GB membership to shadowed GB
• Figure 3: The changes of uncertainty variance and fuzziness when $\alpha$ changes
• Figure 4: Three-way classification based on shadowed GBs
• Figure 5: The comparison with three-way classifiers under different noise rates

Theorems & Definitions (13)

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