Mathematical analysis of generative adversarial networks based on complex picture fuzzy soft information

Generative Adversarial Networks (GANs) are the models that generate data samples from the statistical distribution of the data. It is one of the most well-known branches of machine learning and deep learning. Different techniques are involved in the processing and production of visual data, which sometimes gives rise to misperception uncertainties. Bearing this issue in mind, we define some solid mathematical concepts to model and resolve the stated problem named complex picture fuzzy soft relations (CPFSRs) which is defined by the Cartesian product (CP) of two complex picture fuzzy soft sets (CPFSSs). The major objective of this study is to develop some innovative and useful notions that may be used to handle difficult and inconsistent information in practical situations. The proposed notion is foremost and superior to the prevailing ideas, where the presented idea is the improved technique of two different theories, named picture fuzzy set (PFS) and soft set (SS). Additionally, it presents the picture fuzzy soft set (PFSS) in professional decision-making by reducing complexions. The evaluated CPFSRs are the improved versions of soft relations, fuzzy relations, complex soft relations, and complex fuzzy relations. Therefore, this paper provides modeling methodologies based on CPFSRs which are used for the analysis of electing the best GAN for effective working. In the process, the score functions are also formulated and analyzed. Finally, a comparative study of existing techniques has been done to show the validity of the proposed work.