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<p>This paper focuses on the theory and properties of <i>M</i>-hazy semigroups based on <i>M</i>-hazy operations. First, leveraging <i>M</i>-hazy binary operation, we define <i>M</i>-hazy semigroups and introduce the concepts of commutative law, zero element and identity element. Subsequently, we define pointwise mappings from fuzzy points to fuzzy points and investigate the relationship between <i>M</i>-hazy pointwise mappings and classical mappings. Next, we introduces the notions of subsemigroups, ideals, homomorphisms, weak homomorphisms and isomorphisms for <i>M</i>-hazy semigroups. Building on these foundations, we prove the <i>M</i>-hazy faithful representation theorem for <i>M</i>-hazy semigroups. Finally, we define <i>M</i>-hazy rectangular bands and extend <i>M</i>-hazy pointwise mappings to two-dimensional spaces, thereby deriving fundamental properties of <i>M</i>-hazy rectangular bands.</p>

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M-hazy semigroups

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Yifan Zhai,
  • Qi Liu

摘要

This paper focuses on the theory and properties of M-hazy semigroups based on M-hazy operations. First, leveraging M-hazy binary operation, we define M-hazy semigroups and introduce the concepts of commutative law, zero element and identity element. Subsequently, we define pointwise mappings from fuzzy points to fuzzy points and investigate the relationship between M-hazy pointwise mappings and classical mappings. Next, we introduces the notions of subsemigroups, ideals, homomorphisms, weak homomorphisms and isomorphisms for M-hazy semigroups. Building on these foundations, we prove the M-hazy faithful representation theorem for M-hazy semigroups. Finally, we define M-hazy rectangular bands and extend M-hazy pointwise mappings to two-dimensional spaces, thereby deriving fundamental properties of M-hazy rectangular bands.