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T-Fuzzy Structure on JU-Algebra.

Selamawit Hunie Gelaw1,2, Berhanu Assaye Alaba1, Mihret Alamneh Taye1

  • 1Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia.

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Summary
This summary is machine-generated.

This study introduces T-fuzzy JU-subalgebras and JU-ideals using T-norms, exploring their properties. Findings confirm that Cartesian products of these fuzzy structures maintain their subalgebra and ideal properties.

Keywords:
Cartesian productJU-algebraT-Fuzzy JU-IdealsT-fuzzy JU-subalgebraT-norm

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Area of Science:

  • Fuzzy Mathematics
  • Abstract Algebra

Background:

  • Fuzzy algebra extends classical algebra using fuzzy set theory.
  • JU-algebras are algebraic structures with specific properties.
  • T-norms are functions used in fuzzy set theory to generalize the concept of 'and'.

Purpose of the Study:

  • To define and investigate T-fuzzy JU-subalgebras and JU-ideals.
  • To characterize idempotent T-fuzzy JU algebras.
  • To analyze the behavior of these fuzzy structures in Cartesian products.

Main Methods:

  • Definition of T-fuzzy JU-subalgebras and JU-ideals based on T-norm operations.
  • Theoretical analysis of structural properties.
  • Characterization of idempotent cases.
  • Construction of Cartesian products to prove closure properties.

Main Results:

  • Idempotent T-fuzzy JU algebras exhibit distinct structural characteristics.
  • The Cartesian product of T-fuzzy JU-subalgebras is also a T-fuzzy JU-subalgebra.
  • The Cartesian product of T-fuzzy JU-ideals is also a T-fuzzy JU-ideal.

Conclusions:

  • The study successfully extends the theoretical framework of fuzzy algebra.
  • The closure properties of T-fuzzy JU-subalgebras and JU-ideals under Cartesian products are established.
  • The findings have implications for further research in fuzzy algebraic structures.