Hybrid integrated decision-making algorithm for clustering analysis based on a bipolar complex fuzzy and soft sets

Abstract

Data clustering is an instrumental tool in the area of energy management resources, marketing, and business. Clustering helps to increase productivity, facilitate decision-making, and generate new business opportunities. On the other hand, the soft set theory provides a general mathematical tool for dealing with uncertain, and vague information. In this paper, we present the novel concept of the BCIFSSs (“bipolar complex intuitionistic fuzzy soft sets”) by merging bipolar complex intuitionistic fuzzy sets and soft sets. Also, we explain their basic operations including complement, union, and intersection with some appropriate examples. The involvement of complex numbers enables these structures to cope with phase-altering problems and multidimensional problems for handling ambiguity. Further, the BCIFSSs have an extensive structure because it discusses both grades of memberships (Mem-S) and non-memberships (Non-Mem-S) with positive and negative aspects and can also deal with multivariable difficulties. Later on, we stated a decision-making algorithm and real-world examples to demonstrate the effectiveness, and applicability of the proposed concept. The BCIFSSs show the dual grades of both the Mem-S and Non-Mem-S in the decision-making process. Finally, the comparative analysis of introduced frameworks with some pre-existing ideas is given.