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Bipolar Fuzzy Pseudo-UP Ideal Of Pseudo-UP Algebra
Alachew Amaneh Mechderso1, Berhanu Assaye Alaba1, Tilahun Mekonnen Munie1
1Department of Mathematics, Bahir Dar University College of Science, Bahir Dar, Amhara, 6000, Ethiopia.
F1000Research
|February 11, 2025
Summary
This study explores bipolar fuzzy sets applied to pseudo-UP ideals in pseudo-UP algebras. It demonstrates that intersections of these ideals are preserved, but unions are not, and examines properties under homomorphisms and Cartesian products.
Area of Science:
- Algebraic Structures
- Fuzzy Set Theory
- Mathematical Logic
Background:
- Pseudo-UP algebras are an algebraic structure with specific properties.
- Bipolar fuzzy sets offer a generalized framework for representing uncertainty.
- Understanding ideal structures within algebraic systems is crucial for theoretical advancements.
Purpose of the Study:
- To introduce and investigate the concept of bipolar fuzzy pseudo-UP ideals in pseudo-UP algebras.
- To analyze the closure properties of bipolar fuzzy pseudo-UP ideals under set operations.
- To explore the behavior of these ideals under algebraic mappings like homomorphisms and Cartesian products.
Main Methods:
- Application of bipolar fuzzy set theory to the definition of pseudo-UP ideals.
- Proof-based mathematical derivations to establish properties of these ideals.
- Investigation of homomorphisms and Cartesian products in the context of bipolar fuzzy pseudo-UP ideals.
Main Results:
- The intersection of two bipolar fuzzy pseudo-UP ideals is always a bipolar fuzzy pseudo-UP ideal.
- The union of two bipolar fuzzy pseudo-UP ideals is not necessarily a bipolar fuzzy pseudo-UP ideal.
- Properties of homomorphic images, inverse images, and Cartesian products of bipolar fuzzy pseudo-UP ideals were established.
Conclusions:
- Bipolar fuzzy pseudo-UP ideals exhibit specific closure properties under intersection and Cartesian products.
- Homomorphism and Cartesian product operations preserve the structure of bipolar fuzzy pseudo-UP ideals.
- This research contributes to the understanding of fuzzy structures in abstract algebra.
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