Abstract
In this paper, we introduce a new function on fuzzy real numbers, defined on the set of fuzzy real numbers \({\mathbb {R}}^n,\) which represents both a fuzzy real number and a new concept of a square root at the same time. We call it “delta root.” The definition of the square root in the fuzzy real number system has been suggested based on the \(\alpha \)-level set. So, it has some drawback that cannot represent the extension of the square root in the real number system, but the delta root is a natural extension of the square root of real numbers, which are shown from the properties in this paper. Moreover, we prove that the delta root of fuzzy real numbers is equivalent to the square root of fuzzy real numbers.
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Acknowledgements
The first author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2018R1D1A1A02047995). The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1002653). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1A01011131).
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Communicated by Yichuan Yang.
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Byun, T., Lee, J.E. & Yoon, J.H. Delta root: a new definition of a square root of fuzzy numbers. Soft Comput 26, 4163–4169 (2022). https://doi.org/10.1007/s00500-022-06808-3
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DOI: https://doi.org/10.1007/s00500-022-06808-3