Affiliations: [a] Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
| [b] Department of Computer Science and Automated Systems, Belgorod Shoukhov State University of Technology, Belgorod, Russia | [c] Department of Mathematics, COMSATS University Islamabad, Islmabad Campus, Pakistan; Department of Mathematics, The University of Agriculture, Dera Ismail Khan, Pakistan
Correspondence:
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Corresponding author. Muhammad Zeeshan, E-mail: [email protected].
Abstract: In this paper, we have discussed some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we developed the basic results of CFSs under the basic operations such as complex fuzzy simple difference, bounded sum, bounded difference, dot product, bounded product, union, intersection, and Cartesian product. We explored the CFSs and discussed the related properties with examples such as complex fuzzy bounded sum over the intersection, complex fuzzy dot product over the union, etc. Identifying the reference signals under the environment of CFSs have always been a challenging. Many algorithms based on set theoretic operations and distance measures have been proposed for identifying a reference signal using any common system. But linear time invariant (LTI) system is considered easy to analyze the linear and time-varying signals. We used CFSs in signals and systems. We developed an algorithm based on convolution product and LTI system under the complex fuzzy environment. We identified a high degree of resemblance (reference signal) of the received signals to the reference signal in a linear time-invariant (LTI) system that receives an input signal and produces an output signal.
Keywords: Complex fuzzy sets, inverse discrete Fourier transform, signals and systems, linear-time invariant (LTI) system
