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<p>The centroid, a fundamental reference for ordering fuzzy numbers, is characterized by its horizontal and vertical coordinates, reflecting fuzzy numbers' strengths and weaknesses. We define the preferred two-dimensional centroid for generalized fuzzy numbers. By leveraging the membership function characteristics of the generalized trapezoidal fuzzy number (GTrFN) and a specific basic unit-interval monotonic (BUM) function, analytical expressions for this centroid are derived. Theorems and properties of the proposed centroid are verified, showing that it degenerates to the two-dimensional centroid introduced by Wang et al. (Fuzzy Sets Syst 157(7):919–926, 2006), thus demonstrating strong degradation compatibility. Secondly, a method for characterizing quantitative and qualitative attributes as GTrFNs in incomplete samples is developed, which better captures the true characteristics of attribute information and unifies heterogeneous attributes. A similarity measure between GTrFNs is defined based on the preferred two-dimensional centroid, effectively reflecting preference similarity through geometric distance differences. This study proposes a heterogeneous generalized fuzzy multi-attribute decision-making method based on a preferred two-dimensional centroid (PTC-HFMADM method), aiming to enhance the realistic portrayal of decision information and incorporate decision-makers' (DMs) risk preferences. Finally, the method's effectiveness and feasibility are illustrated through a comprehensive evaluation of forestland quality across various townships.</p>

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Decision-making method with large-scale heterogeneous information using the preferred two-dimensional centroid and its application in forestland quality evaluation

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Huizhen Cai,
  • Jian Lin,
  • Zhongzhu Chen,
  • Zeshui Xu

摘要

The centroid, a fundamental reference for ordering fuzzy numbers, is characterized by its horizontal and vertical coordinates, reflecting fuzzy numbers' strengths and weaknesses. We define the preferred two-dimensional centroid for generalized fuzzy numbers. By leveraging the membership function characteristics of the generalized trapezoidal fuzzy number (GTrFN) and a specific basic unit-interval monotonic (BUM) function, analytical expressions for this centroid are derived. Theorems and properties of the proposed centroid are verified, showing that it degenerates to the two-dimensional centroid introduced by Wang et al. (Fuzzy Sets Syst 157(7):919–926, 2006), thus demonstrating strong degradation compatibility. Secondly, a method for characterizing quantitative and qualitative attributes as GTrFNs in incomplete samples is developed, which better captures the true characteristics of attribute information and unifies heterogeneous attributes. A similarity measure between GTrFNs is defined based on the preferred two-dimensional centroid, effectively reflecting preference similarity through geometric distance differences. This study proposes a heterogeneous generalized fuzzy multi-attribute decision-making method based on a preferred two-dimensional centroid (PTC-HFMADM method), aiming to enhance the realistic portrayal of decision information and incorporate decision-makers' (DMs) risk preferences. Finally, the method's effectiveness and feasibility are illustrated through a comprehensive evaluation of forestland quality across various townships.