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Fuzzy Set Theory Applied on Autometrized Algebra
1Department of Mathematics, Assosa University, Asosa, Benishangul-Gumuz, Ethiopia.
F1000Research
|March 3, 2025
Summary
This study explores fuzzy subalgebras and fuzzy ideals within autometrized algebras. A key finding establishes a one-to-one correspondence between fuzzy ideals and fuzzy congruences in normal autometrized algebras.
Area of Science:
- Algebraic Structures
- Fuzzy Set Theory
Background:
- Autometrized algebras are algebraic structures with specific metric properties.
- Fuzzy set theory extends classical set theory to handle uncertainty and vagueness.
Purpose of the Study:
- To introduce and investigate fuzzy subalgebras and fuzzy ideals in the context of autometrized algebras.
- To analyze the behavior of homomorphisms concerning fuzzy subalgebras and ideals.
- To define and explore fuzzy congruences on autometrized algebras.
Main Methods:
- Introduction of fuzzy subalgebra and fuzzy ideal concepts tailored for autometrized algebras.
- Examination of image and inverse image properties under homomorphisms.
- Development of the theory of fuzzy congruences.
Main Results:
- Properties of fuzzy subalgebras and fuzzy ideals are studied.
- Homomorphisms of fuzzy subalgebras and ideals are analyzed.
- A one-to-one correspondence is proven between fuzzy ideals and fuzzy congruences in normal autometrized algebras.
Conclusions:
- The paper successfully extends fuzzy algebraic concepts to autometrized algebras.
- The established correspondence provides a significant structural insight into these algebras.
- This work lays the foundation for further research in fuzzy algebraic structures.
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