Fuzzy quantification-driven Three-way decision: model, algorithm and application

Lu Wang

doi:10.1016/j.cnsns.2026.110921

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Fuzzy quantification-driven Three-way decision: model, algorithm and application

2026-10-06

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Lu Wang

Lingqiang Li *

DOI：10.1016/j.cnsns.2026.110921

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Abstract

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Three-way decision (TWD) is an uncertain decision-making framework derived from probabilistic rough set theory. It adopts the ternary strategy of accept-reject-delay, which can effectively reduce decision-making risks and improve the rationality of decisions. Fuzzy quantification, a novel fuzzy logic method, facilitates constructing optimization models with high interpretability and strong anti-interference ability. Recently, we find that the conditional probability in TWD can be defined through specific fuzzy quantification method. Based on this finding, we propose a novel fuzzy quantification-driven TWD. First, we design a family of fuzzy quantifiers with strong convergence properties, and based on this family of operators, we define a new type of conditional probability, which is named quantized Λ-conditional probability. Theoretical proofs demonstrate that this conditional probability not only includes traditional conditional probability as a special case, but also takes it as a convergence limit. Second, by integrating utility theory, a new TWD model is constructed with the criterion of maximum utility, along with corresponding algorithms. Finally, we conducted experiments applying TWD to classification problems on 13 open-source datasets, using a stratified 5-fold cross-validation strategy. The results demonstrate that the proposed method exhibits excellent stability and robustness across three key metrics: Precision, F1 score, and Balanced accuracy. Compared with five state-of-the-art methods proposed in 2024-2025, statistical validation confirms that the proposed method achieves an average improvement of approximately 13.48% across three metrics. In conclusion, the proposed quantified TWD method broadens the theoretical foundation of TWD while exhibiting superior classification performance in practical applications.