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Complex fuzzy sets with applications in signals

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Abstract

A complex fuzzy set is characterized by a membership function, whose range is not limited to [0, 1], but extended to the unit circle in the complex plane. In this paper, we introduce some new operations and laws of a complex fuzzy set such as disjunctive sum, simple difference, bounded difference, distributive law of union over intersection and intersection over union, equivalence formula, symmetrical difference formula, involution law, absorption law, and idempotent law. We introduce some basic results on complex fuzzy sets with respect to standard complex fuzzy intersection, union, and complement functions corresponding to the same functions for determining the phase term, and we give particular examples of these operations. We use complex fuzzy sets in signals and systems, because its behavior is similar to a Fourier transform in certain cases. Moreover, we develop a new algorithm using complex fuzzy sets for applications in signals and systems by which we identify a reference signal out of large number of signals detected by a digital receiver. We use the inverse discrete Fourier transform of a complex fuzzy set for incoming signals and a reference signal. Thus, a method for measuring the exact values of two signals is provided by which we can identity the reference signal.

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Acknowledgements

The authors are thankful to associate editor Marcos Eduardo Valle and anonymous referees for their valuable comments on our manuscript. This research is partially supported by NNSFC (61866011; 11561023). The third author is thankful to Higher Education Commission of Pakistan for the financial support.

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Authors and Affiliations

  1. Department of Mathematics, Hubei Minzu University, Enshi, 445000, Hubei, China

    Xueling Ma & Jianming Zhan

  2. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Islamabad, Pakistan

    Madad Khan, Muhammad Zeeshan, Saima Anis & Abdul Sami Awan

Authors
  1. Xueling Ma
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  2. Jianming Zhan
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  3. Madad Khan
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  4. Muhammad Zeeshan
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  5. Saima Anis
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  6. Abdul Sami Awan
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Correspondence to Jianming Zhan.

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Communicated by Marcos Eduardo Valle.

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Ma, X., Zhan, J., Khan, M. et al. Complex fuzzy sets with applications in signals. Comp. Appl. Math. 38, 150 (2019). https://doi.org/10.1007/s40314-019-0925-2

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