Fuzzy filter on BI-algebras

Document Type : Original Article

Author

Payame Noor University Department of Mathematics p.o.box 19395-3697, Tehran,

10.22034/jfsa.2024.408512.1182

Abstract

In this paper, the concepts of fuzzy filter and fuzzy sub-algebra on BI-algebras are introduced. Then some of their properties are investigated. Fuzzy sub-algebras and fuzzy filters are classified according to level sets and equivalent definitions for fuzzy filters are provided. It has also been proven that in every distributive BI-algebra, every filter is a sub-algebra and we have shown that in a group of BI-algebras, every subset contains 1 is a sub-algebra and every fuzzy subset that satisfies the first condition of the filter is a fuzzy filter. Moreover, it is proved that the set of all fuzzy filters on BI-algebras is a complete lattice. The relation of congruence and quotient BI-algebra produced by fuzzy filters is also investigated.

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References

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Fuzzy Systems and its Applications
Volume 6, Issue 2 - Serial Number 13
January 2024
Pages 167-190

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History

  • Receive Date: 24 July 2023
  • Revise Date: 18 September 2023
  • Accept Date: 28 January 2024

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