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<p>Multiple-criteria decision-making (MCDM) under heterogeneous and incomplete information remains a persistent challenge, as most existing methods require preprocessing steps such as homogenization or imputation. These steps often distort the underlying data and may lead to biased outcomes. To address this limitation, this study introduces the incomplete neighborhood soft set (INSS), a new framework that explicitly accommodates missing values and mixed-type attributes. Building on this, we define the Incomplete Neighborhood Soft Decision System (INSDS) and propose a dependency-based attribute reduction scheme that preserves decision-relevant information without the need for data completion and transformation. We further integrate INSS with the Naïve Bayes Classifier (NBC), yielding the INSS-NBC decision model, which allows direct analysis of heterogeneous and incomplete datasets. The proposed approach is evaluated on a loan default prediction task and compared against NBC models combined with standard preprocessing techniques, including principal component analysis, factor analysis, LASSO, and random forest selection. Results indicate that INSS-NBC achieves superior predictive performance while avoiding assumptions about the data-generating mechanism. Overall, the findings highlight the potential of INSS as a general representation for imperfect information and demonstrate the feasibility and robustness of INSS-NBC in practical MCDM applications.</p>

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A decision-making method based on the neighborhood soft set and Bayes classifier under a heterogeneous and incomplete information environment

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Sisi Xia,
  • Lin Chen,
  • Siya Liu

摘要

Multiple-criteria decision-making (MCDM) under heterogeneous and incomplete information remains a persistent challenge, as most existing methods require preprocessing steps such as homogenization or imputation. These steps often distort the underlying data and may lead to biased outcomes. To address this limitation, this study introduces the incomplete neighborhood soft set (INSS), a new framework that explicitly accommodates missing values and mixed-type attributes. Building on this, we define the Incomplete Neighborhood Soft Decision System (INSDS) and propose a dependency-based attribute reduction scheme that preserves decision-relevant information without the need for data completion and transformation. We further integrate INSS with the Naïve Bayes Classifier (NBC), yielding the INSS-NBC decision model, which allows direct analysis of heterogeneous and incomplete datasets. The proposed approach is evaluated on a loan default prediction task and compared against NBC models combined with standard preprocessing techniques, including principal component analysis, factor analysis, LASSO, and random forest selection. Results indicate that INSS-NBC achieves superior predictive performance while avoiding assumptions about the data-generating mechanism. Overall, the findings highlight the potential of INSS as a general representation for imperfect information and demonstrate the feasibility and robustness of INSS-NBC in practical MCDM applications.