Amplitude interval-valued complex Pythagorean fuzzy sets with applications in signals processing

Article type: Research Article

Authors: Zeeshan, Muhammad^{a; *} | Khan, Madad^b | Iqbal, Sohail^a

Affiliations: [a] Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Pakistan | [b] Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan

Correspondence: [*] Corresponding author. Muhammad Zeeshan, Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Pakistan. E-mail: zeeshan.msc08@gmail.com.

Abstract: In this paper, we introduce the notion of amplitude interval-valued complex Pythagorean fuzzy sets (AIVCPFSs). The motivation for this extension is the utility of interval-valued complex fuzzy sets in membership and non-membership degree which can express the two dimensional ambiguous information as well as the interaction among any set of parameters when they are in the form of interval-valued. The principle of AIVCPFS is a mixture of the two separated theories such as interval-valued complex fuzzy set and complex Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real part is the sub-interval of the unit interval. We discuss some set-theoretic operations and laws of the AIVCPFSs. We study some particular examples and basic results of these operations and laws. We use AIVCPFSs in signals and systems because its behavior is similar to a Fourier transform in certain cases. Moreover, we develop a new algorithm using AIVCPFSs for applications in signals and systems by which we identify a reference signal out of the large number of signals detected by a digital receiver. We use the inverse discrete Fourier transform for the membership and non-membership functions of AIVCPFSs for incoming signals and a reference signal. Thus a method for measuring the resembling values of two signals is provided by which we can identify the reference signal.

Keywords: Amplitude interval-valued complex Pythagorean fuzzy set, Complex fuzzy set, Fuzzy set, Inverse discrete Fourier transform

DOI: 10.3233/JIFS-212615

Journal: Journal of Intelligent & Fuzzy Systems, vol. 43, no. 1, pp. 907-925, 2022