Complex Intuitionistic Fuzzy N-Soft Sets and Their Applications in Decision Making Algorithm

Abstract

Complex intuitionistic fuzzy sets (CIFSs) and N-soft sets (N-SSs) are the generalized models of fuzzy sets (FSs) and soft sets (SSs) respectively, to deal with unknown and complicated data in the problems of real-life. This study initiates a novel concept of complex intuitionistic fuzzy N-soft sets (CIFN-SSs), which is a mixture of two different models, called CIFSs and N-SSs. CIFN-SSs can be seen as a modified N-SS based on the CIFSS. CIFN-SS is more generalized tool as compared to the existing ones. Moreover, we initiate some basic properties along with their basic operations and illustrate them with the help of examples. Further, we initiate the relationship of our novel model with existing models like complex intuitionistic fuzzy soft sets (CIFSSs) and SS. Additionally, to show the credibility and effectiveness of our initiated model, we apply it to decision-making (DM) problems of real life. We also define an algorithm to solve DM problems by using CIFN-SS. Finally, we compare our novel approach with the existing model intuitionistic fuzzy N-SS (IFN-SS) to show the supremacy of our initiated concept.