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<p>In engineering, the development of a comprehensive system model often involves integrating multiple subsystem models like fuzzy systems and radial basis function neural networks (RBFNs). Fuzzy systems use fuzzy rules to define behavioral regions, while RBFNs respond to specific input regions. Effective partitioning of these models into subsystems employs various clustering approaches, based on data characteristics or the system’s local behavior. These approaches can be partitional or hierarchical, with some relying on regression-based error metrics instead of traditional distance-based methods. This is crucial when handling complex data structures such as interval-valued data, probability density functions, or categorical data. Symbolic Data Analysis (SDA) has developed methods for these challenges, including generalized distance measures and interval-valued clustering approaches. This study proposes an interval fuzzy <i>c</i>-bivariate regression model with a Box–Cox transformation (iFCBRMbc) clustering approach. The iFCBRMbc partitions the overall linear interval regression model into multiple sub-models, facilitating the identification of linear interval regression coefficients. Regression model errors replace traditional distance-based criteria in the clustering process. The Box–Cox transformation normalizes skewed interval-valued data, essential for preventing performance deterioration in linear interval-valued regression models. Integrating a bivariate linear interval regression model enhances the performance of these models. The estimated output is calculated by combining the outputs of multiple regression models with their fuzzy membership degrees. The effectiveness and performance of the proposed iFCBRMbc clustering approach are validated using real datasets.</p>

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Interval Fuzzy c-Bivariate Regression Models with Box–Cox Transformation Clustering Approach for the Interval-Valued Data

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Jin-Tsong Jeng,
  • Chen-Chia Chuang,
  • Tzu-Yun Lin

摘要

In engineering, the development of a comprehensive system model often involves integrating multiple subsystem models like fuzzy systems and radial basis function neural networks (RBFNs). Fuzzy systems use fuzzy rules to define behavioral regions, while RBFNs respond to specific input regions. Effective partitioning of these models into subsystems employs various clustering approaches, based on data characteristics or the system’s local behavior. These approaches can be partitional or hierarchical, with some relying on regression-based error metrics instead of traditional distance-based methods. This is crucial when handling complex data structures such as interval-valued data, probability density functions, or categorical data. Symbolic Data Analysis (SDA) has developed methods for these challenges, including generalized distance measures and interval-valued clustering approaches. This study proposes an interval fuzzy c-bivariate regression model with a Box–Cox transformation (iFCBRMbc) clustering approach. The iFCBRMbc partitions the overall linear interval regression model into multiple sub-models, facilitating the identification of linear interval regression coefficients. Regression model errors replace traditional distance-based criteria in the clustering process. The Box–Cox transformation normalizes skewed interval-valued data, essential for preventing performance deterioration in linear interval-valued regression models. Integrating a bivariate linear interval regression model enhances the performance of these models. The estimated output is calculated by combining the outputs of multiple regression models with their fuzzy membership degrees. The effectiveness and performance of the proposed iFCBRMbc clustering approach are validated using real datasets.