Abstract
In this paper, we established some new operations and formulas of set theory for complex fuzzy sets (CFSs). We introduced the basic results of CFSs with their examples using union, intersection, complement, dot product, complex fuzzy probalistic sum, complex fuzzy bold sum, complex fuzzy bold sum over associative law of union, etc. Moreover, we introduced an algorithm to identify a reference signal out of large number of signal having bigger N \(\left( {Samples} \right)\) received by a digital receiver. Thus, a new model is introduced for measuring the values of the signals in a faster way using CFSs.
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References
Atanassove K (1986) Intuitionistic fuzzy fets. Fuzzy Sets Syst 20:87–90
Bo H, Bi L (2017) The orthogonality between complex fuzzy sets and its application to signal detection. Symmetry 9:175
Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex Fourier series. Math Comput 19:297–301
Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic, theory and applications. Prentice Hall, New Jersey
Khan M, Anis S (2020) Complex fuzzy soft matrices with applications. Hacet J Math Stat 49(2):676–683
Ma X, Zhan J, Khan M, Anis S, Zeeshan M, Sami Awan A (2019) Complex fuzzy sets with applications in signals. Comput Appl Math 38:150
Mandel JM (1995) Fuzzy logic systems for engineering, A tutorial. Proc IEEE 83:345–377
Naz S, Akram M (2019) Novel decision making approach based on hesitant fuzzy sets and graph theory. Comput Appl Math 38:7
Paul H (1995) Fourier transform and fast Fourier transform algorithm. Notes Comput Graph 2:15–643
Poodeh Y (2017) Applications of complex fuzzy sets in time series prediction, Ph.D thesis. University of Alberta
Ramot D, Milo R (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186
IW Selenick, G Schullar (2001) The Discrete Fourier Transform, Second chapter of the book The transform and data compression Handbook, editted by. K. R. Rao and CRC, Press, Boca Raton
Suto J, Oniga S (2015) A new relation between Twiddle factor in the Fast Fourier transform. Elektronika Ir Electrotechnika 21(4):1392–1215
Yazdanbakhsh O, Dick S (2018) A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst 338:1–22
Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353
Zimmermann LA (1991) Fuzzy set theory- and its application, 2nd edn. Kluwer, Boston
Zhang G (2009) Operation properties and equalities of complex fuzzy sets. Int J Approx Reason 50:1227–1249
Acknowledgements
This work is financially supported by the Higher Education Commission of Pakistan (Grant No: 7750/Federal/ NRPU/R&D/HEC/ 2017).
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Khan, M., Khan, I., Fahmi, A. et al. A faster algorithm for identifying signals using complex fuzzy sets. Soft Comput 26, 7059–7079 (2022). https://doi.org/10.1007/s00500-022-07132-6
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DOI: https://doi.org/10.1007/s00500-022-07132-6