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Hesitant Fuzzy Subalgebras, Ideals and Congruences on Autometrized Algebras
1Department of Mathematics, Assosa University, Asosa, Benishangul-Gumuz, Ethiopia.
F1000Research
|September 22, 2025
Summary
This study explores hesitant fuzzy subalgebras and ideals within autometrized algebras. Researchers established key properties and introduced hesitant fuzzy congruences for these algebraic structures.
Area of Science:
- Algebraic Structures
- Fuzzy Set Theory
- Mathematical Analysis
Background:
- Autometrized algebras are a generalization of metric spaces.
- Fuzzy set theory provides tools for handling uncertainty.
- Hesitant fuzzy sets allow for multiple membership values.
Purpose of the Study:
- To introduce and investigate hesitant fuzzy subalgebras of autometrized algebras.
- To define and analyze hesitant fuzzy ideals in this context.
- To explore hesitant fuzzy congruences and related concepts on autometrized algebras.
Main Methods:
- Definition and exploration of hesitant fuzzy subalgebras.
- Examination of properties of hesitant fuzzy ideals.
- Introduction and analysis of hesitant fuzzy congruences.
- Investigation of characteristic equations and level subsets.
Main Results:
- Properties of hesitant fuzzy subalgebras were derived.
- The concept of hesitant fuzzy ideals was introduced and studied.
- Hesitant fuzzy congruences were defined and their properties discussed.
- Characteristic equations and level subsets for hesitant fuzzy sets and relations were presented.
Conclusions:
- The paper successfully extends the study of fuzzy structures to autometrized algebras using hesitant fuzzy sets.
- New theoretical frameworks for hesitant fuzzy subalgebras, ideals, and congruences were established.
- The findings contribute to the understanding of algebraic structures with uncertainty quantification.
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