Enhanced MCDM Based on the TOPSIS Technique and Aggregation Operators Under the Bipolar pqr-Spherical Fuzzy Environment: An Application in Firm Supplier Selection

Multiple criteria decision-making (MCDM) is a significant area of decision-making theory that certainly warrants attention. It might be difficult to accurately convey the necessary decision facts when navigating decision-making problems since we frequently run into complicated issues and unpredictable situations. To address this, introducing the novel idea of the bipolar pqr-spherical fuzzy set (BpqrSFS), a hybrid structure of the bipolar fuzzy set (BFS) and the pqr-spherical fuzzy set (pqr-SFS), is the main goal of this work. The fundamental (set-theoretic and algebraic) operations on BpqrSFSs are explained as well as their relations to several known models. A distance measure, such as Euclidean distance, among BpqrSFNs, is provided. Afterward, we expand the fundamental aggregation operators to the pqr-spherical fuzzy (BpqrSF) environment by developing bipolar pqr-spherical fuzzy-weighted averaging and bipolar pqr-spherical fuzzy-weighted geometric operators for aggregating BpqrSFNs. According to the aforementioned distance measure and operators, an MCDM approach is established consisting of two algorithms, namely, the TOPSIS method and the method using the proposed operators in the BpqrSF context. Moreover, a numerical example is provided in order to ensure that the presented model is applicable. By using the two algorithms, a comparative analysis of the proposed method with other existing ones is given in order to verify the feasibility of the suggested decision-making procedure.