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<p>In this paper, we introduce the concept of the ordinal sum for families of uninorms and investigate the natural fuzzy negation induced by a uninorm, with particular emphasis on convex sums. We establish necessary and sufficient conditions under which the ordinal sum of a family of uninorms is itself a uninorm. Additionally, we derive results concerning ordinal sums constructed from families of uninorms based on the underlying t-norms and t-conorms. We further generalize two well-known families of uninorms and analyze the natural negation associated with ordinal sums within this broader class.</p>

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Natural fuzzy negations and ordinal sums of uninorms

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Ivan Mezzomo,
  • Benjamin Bedregal,
  • Thadeu Milfont,
  • Matheus da Silva Menezes

摘要

In this paper, we introduce the concept of the ordinal sum for families of uninorms and investigate the natural fuzzy negation induced by a uninorm, with particular emphasis on convex sums. We establish necessary and sufficient conditions under which the ordinal sum of a family of uninorms is itself a uninorm. Additionally, we derive results concerning ordinal sums constructed from families of uninorms based on the underlying t-norms and t-conorms. We further generalize two well-known families of uninorms and analyze the natural negation associated with ordinal sums within this broader class.