Abstract
This article aims to link AG-groupoids and complex fuzzy set theory by constructing a method to rank complex fuzzy information, provide an alternative definition of CLDFS, and an algorithm for data encryption/decryption using AG-groupoids. Achieving these objectives would enable effective handling of complex and ambiguous data and a novel approach to data security with potential applications in various industries. The authors introduce new operations and laws to explore the structural properties of CLDFS, including applying the inverse discrete Fourier transform of a CLDFS to identify a reference signal and characterizing right regular ordered AG-groupoids in terms of CLDF-score right ideals. They also demonstrate an application of utilizing an AG-groupoid as a symmetric key for encryption/decryption and CLDF-score right ideals of an ordered AG-groupoid to select a suitable signal for system analysis.
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