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<p>We show that fuzzy ideal lattices and fuzzy congruence lattices on basic algebras are not one–one correspondent in the sense of Murali. Then we define fuzzy (weak, respectively) congruence relations on basic algebras in a new way, which guarantees the one–one correspondence between fuzzy (weak, respectively) ideal lattices and fuzzy (weak, respectively) congruence lattices on basic algebras.</p>

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Fuzzy congruences and ideals on basic algebras

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Jing Wang,
  • Qiuyan Zhan,
  • Yichuan Yang

摘要

We show that fuzzy ideal lattices and fuzzy congruence lattices on basic algebras are not one–one correspondent in the sense of Murali. Then we define fuzzy (weak, respectively) congruence relations on basic algebras in a new way, which guarantees the one–one correspondence between fuzzy (weak, respectively) ideal lattices and fuzzy (weak, respectively) congruence lattices on basic algebras.