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This paper explores interaction operators utilized within the framework of the inclusion and exclusion integral (IE-integral). Specifically, we introduce a novel duality concept for interaction operators and the associative and commutative binary operators (AC-operators) that produce them. These concepts are derived from the conventional duality of set functions through the framework of IE-integrals. Moreover, we reframe IE-integrals and the aforementioned new concepts from the standpoint of discrete derivatives.

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A New Duality Concept for AC and Interaction Operators Through the IE-Integral

  • 会议论文

  • 发表日期：

    2025年

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  • Katsushige Fujimoto,
  • Aoi Honda

摘要

This paper explores interaction operators utilized within the framework of the inclusion and exclusion integral (IE-integral). Specifically, we introduce a novel duality concept for interaction operators and the associative and commutative binary operators (AC-operators) that produce them. These concepts are derived from the conventional duality of set functions through the framework of IE-integrals. Moreover, we reframe IE-integrals and the aforementioned new concepts from the standpoint of discrete derivatives.