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Pythagorean fuzzy deductive system of BCL-algebra.
Asmamaw Abebe Biabeyin1, Berhanu Assaye Alaba1, Yohannes Gedamu Wondifraw1
1Mathematics, Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia.
This study introduces Pythagorean fuzzy sets to explore the deductive system of BCL-algebra. The intersection of these fuzzy systems is valid, but their union is not, revealing key properties of fuzzy logic in algebraic structures.
Area of Science:
- Algebraic structures
- Fuzzy set theory
- Mathematical logic
Background:
- The deductive system of BCL-algebra is underexplored.
- Fuzzification of BCL-algebra deductive systems is undefined.
Purpose of the Study:
- Introduce a fuzzy extension of BCL-algebra deductive systems.
- Utilize Pythagorean fuzzy sets for this extension.
Main Methods:
- Define Pythagorean fuzzy sets with membership and non-membership functions.
- Extend classical BCL-algebra deductive systems using fuzzy degrees.
- Incorporate fuzzy operations (union, intersection, complement) and analyze certainty, truth, uncertainty, and deviation.
Main Results:
- Prove that the intersection of two Pythagorean fuzzy deductive systems is valid.
- Demonstrate that the union of Pythagorean fuzzy deductive systems is not always valid.
- Employ induction, logical derivations, and algebraic techniques for proofs.
Conclusions:
- Pythagorean fuzzy deductive systems offer a novel approach to BCL-algebra.
- The intersection property is preserved, but the union property is not, highlighting limitations.
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