Choquet-integrals are averaging aggregation functions based on a fuzzy measure that accounts for both the significance of each attribute being aggregated and the interactions between the variables. The effectiveness of a fuzzy measure can be characterized by its accuracy in modeling the relationship or association degree among the elements to be aggregated. In the literature, it is known that amid conventional fuzzy measures, the Power Measure (PM) presents statistically superior performance. This study explores the q exponent impact in the PM on the performance of different Choquet-based integrals when used in fuzzy rule-based classification systems. We aim to analyze how fixed q values influence classification accuracy across thirty-three benchmark datasets. The updated results reveal that smaller q values (e.g., \(q = 0.1\)  and \(q = 0.5\) ) continue to yield superior accuracy, while larger values ( \(q \ge 100\) ) tend to a performance stabilization. Among the tested methods, the generalization named \(C_{F1F2}\) -integral achieves the highest classification accuracy, effectively adapting to different parameter settings.

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Insights into the q Exponent in Power Measure with Choquet-Based Generalizations for Classification Problems

  • Giancarlo Lucca,
  • Tiago C. Asmus,
  • Cedric Marco-Detchart,
  • Helida S. Santos,
  • Heloisa A. Camargo,
  • Adenauer C. Yamin,
  • Renata H. S. Reiser,
  • Humberto Bustince,
  • Alice Pintanel,
  • Graçaliz P. Dimuro

摘要

Choquet-integrals are averaging aggregation functions based on a fuzzy measure that accounts for both the significance of each attribute being aggregated and the interactions between the variables. The effectiveness of a fuzzy measure can be characterized by its accuracy in modeling the relationship or association degree among the elements to be aggregated. In the literature, it is known that amid conventional fuzzy measures, the Power Measure (PM) presents statistically superior performance. This study explores the q exponent impact in the PM on the performance of different Choquet-based integrals when used in fuzzy rule-based classification systems. We aim to analyze how fixed q values influence classification accuracy across thirty-three benchmark datasets. The updated results reveal that smaller q values (e.g., \(q = 0.1\)  and \(q = 0.5\) ) continue to yield superior accuracy, while larger values ( \(q \ge 100\) ) tend to a performance stabilization. Among the tested methods, the generalization named \(C_{F1F2}\) -integral achieves the highest classification accuracy, effectively adapting to different parameter settings.