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<p>Overlap and grouping functions differ from existing aggregation operators in that they have the advantage of being able to express correlations between aggregated objects. The current multi-granulation fuzzy rough set (MGFRS) constructed with overlap and grouping functions utilize a pair of aggregation operators with duals, which can lead to an increase in computational complexity. In this paper, MGFRS is constructed with a single overlap function or grouping function to achieve a reduction in computational complexity (the upper and lower approximations are non-dual). Therefore, a novel non-dual multi-granulation fuzzy rough set (NDMGFRS) is constructed. The properties of the NDMGFRS model are discussed, and the relationship among this model and other existing MGFRS models is investigated. Based on the NDMGFRS model, two new methods (fuzzy ELECTRE and fuzzy TOPSIS) are applied to multi-attribute group decision making (MAGDM). Finally, through comparative analysis, the ranking results of the two decision-making methods are highly consistent with other decision-making methods, and the model’s validity is verified.</p>

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Non-dual Multi-granulation Fuzzy Rough Sets Based on Overlap and Grouping Functions and Their Applications to MAGDM

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Hongru Bu,
  • Jingqian Wang,
  • Xiaohong Zhang

摘要

Overlap and grouping functions differ from existing aggregation operators in that they have the advantage of being able to express correlations between aggregated objects. The current multi-granulation fuzzy rough set (MGFRS) constructed with overlap and grouping functions utilize a pair of aggregation operators with duals, which can lead to an increase in computational complexity. In this paper, MGFRS is constructed with a single overlap function or grouping function to achieve a reduction in computational complexity (the upper and lower approximations are non-dual). Therefore, a novel non-dual multi-granulation fuzzy rough set (NDMGFRS) is constructed. The properties of the NDMGFRS model are discussed, and the relationship among this model and other existing MGFRS models is investigated. Based on the NDMGFRS model, two new methods (fuzzy ELECTRE and fuzzy TOPSIS) are applied to multi-attribute group decision making (MAGDM). Finally, through comparative analysis, the ranking results of the two decision-making methods are highly consistent with other decision-making methods, and the model’s validity is verified.