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<p>In this paper, we delve into the study of fuzzy number approximation by LR fuzzy numbers, shedding light on their algebraic properties. We present a solid approach to approximate fuzzy numbers keeping the same expected interval and core proving that such approximation is additive and continuous under a wide family of distances. As a key part of this construction, we study the set of fuzzy numbers as a topological monoid and develop a process to embed any cancellative abelian topological monoid with open shifts in a topological abelian group. This allows us to demonstrate a highly useful result in the context of this paper: the continuity of homomorphisms between cancellative topological abelian monoids with open shifts is equivalent to its continuity at zero.</p>

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Examining fuzzy number approximation through a topological algebraic approach

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Hugo J. Bello,
  • Pablo Jimenez,
  • Carlos Bejines

摘要

In this paper, we delve into the study of fuzzy number approximation by LR fuzzy numbers, shedding light on their algebraic properties. We present a solid approach to approximate fuzzy numbers keeping the same expected interval and core proving that such approximation is additive and continuous under a wide family of distances. As a key part of this construction, we study the set of fuzzy numbers as a topological monoid and develop a process to embed any cancellative abelian topological monoid with open shifts in a topological abelian group. This allows us to demonstrate a highly useful result in the context of this paper: the continuity of homomorphisms between cancellative topological abelian monoids with open shifts is equivalent to its continuity at zero.