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TwoFold Algebra
The TwoFold Algebra, with its corresponding TwoFold Law, and their derivatives of Fuzzy (and all fuzzy-extensions) Two Fold Algebras and Laws were introduced by Smarandache [1] in 2024. Although very recent, it is has spread out very fast. Practical applications and several numerical examples were presented as well.
Definition Let's denote by fuzzy-extension theories, all types of fuzzy related theories:
A TwoFold Algebra is formed by two types of algebras: (i) the first algebra is a classical algebra, with respect to the elements x belonging to a given set A;
That's what happens in our real world. Practical Example: Two employees, John and George, work for the same company. John's degree of work quality is 70% (or 0.7) and produces 40 pieces per hour, while George's degree of work quality is 50% (or 0.5) and produces 20 pieces per hour. The manager has observed that what a worker does not do well, the other does better, or the workers complement each other. As such, he had the idea to make them work together as a team, to improve the quality and increase the quantity by 10%. Same thing happened to the other workers in the team, so he decided to organize them to work in teams to improve the quality. John0.7
or
400.7 Therefore, the team John & George produces now 66 pieces of quality 70%, instead of 60 pieces with some of them of lower quality (50%).
References [1] Florentin Smarandache, Neutrosophic TwoFold Algebra, Plithogenic Logic and Computation, 1, 11-15, 2024, https://fs.unm.edu/NeutrosophicTwoFoldAlgebra.pdf [2] Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Randa Bashir Yousef Hijazeen, Mowafaq Omar Al-Qadri, Abdallah Al-Husban, An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers, Neutrosophic Sets and Systems, Vol. 67, 2024, pp. 169-178. DOI: 10.5281/zenodo.11151930, https://fs.unm.edu/TFA/TwoFoldFuzzy11.pdf [3] Hazim M. Wali Al-Tameemi, Fuzzy Metric Spaces Of The Two-Fold Fuzzy Algebra, Neutrosophic Sets and Systems, Vol. 67, 2024, pp. 105-133. DOI: 10.5281/zenodo.11123602, https://fs.unm.edu/TFA/FuzzyMetricSpaces7.pdf [4] Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Mowafaq Omar Al-Qadri, Abdallah Al-Husban, On The Two-Fold Fuzzy n-Refined Neutrosophic Rings For 2≤n≤3, Neutrosophic Sets and Systems, Vol. 68, 2024, pp. 8-25. DOI: 10.5281/zenodo.11406449, https://fs.unm.edu/TFA/TwoFold2.pdf [5] Nabil Khuder Salman, On the Special Gamma Function Over the Complex Two-Fold Algebras, Neutrosophic Sets and Systems, Vol. 68, 2024, pp. 26-38. DOI: 10.5281/zenodo.11406461, https://fs.unm.edu/TFA/SpecialGamma3.pdf [6] Nawar Hazim Mohammed, On The Solutions of Some Different Types of Two-Fold Fuzzy and Neutrosophic Differential Equations, Neutrosophic Sets and Systems, Vol. 70, 2024, pp. 359-368. DOI: 10.5281/zenodo.13177544, https://fs.unm.edu/TFA/TwoFold22.pdf [7] Raed Hatamleh, Ayman Hazaymeh, Finding Minimal Units In Several Two-Fold Fuzzy Finite Neutrosophic Rings, Neutrosophic Sets and Systems, Vol. 70, 2024, pp. 1-16. DOI: 10.5281/zenodo.13160839, https://fs.unm.edu/TFA/FindingMinimal1.pdf
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