Evaluation of Electric Motor Cars Based Frank Power Aggregation Operators Under Picture Fuzzy Information and a Multi-Attribute Group Decision-Making Process

In this article, we expose the notion of power operator to reduce the impact of negative information on the decision-making (DM) process. The power aggregation tools are also robust mathematical aggregation operators (AOs) which allow input arguments to support each other in the DM process. The Frank aggregation expressions are reliable and updated versions of triangular norms which are used to handle complex and complicated information in a decision-making process. The picture fuzzy (PF) set (PFS) is an extended version of the fuzzy sets (FSs) and intuitionistic FSs (IFSs). A PFS has four terms of an object simultaneously such as positive grade (PG), Abstained grade (AG), negative grade (NG) and refusal grade (RG). By using basic operations of Frank aggregation expressions, we propose a list of new appropriate methodologies under consideration of PF information, including picture fuzzy frank power average (PFFPA), and picture fuzzy frank power geometric (PFFPG) operators. We also present some new approaches to PFSs based on Frank aggregation tools such as picture fuzzy frank power weighted average (PFFPWA) and picture fuzzy frank power weighted geometric (PFFPWG) operators. Some appropriate properties and special cases of our currently proposed approaches are also studied. Moreover, to ratify the intensity and reliability of our derived strategies, we illustrated an algorithm of the multi-attribute group decision-making (MAGDM) technique under a PF environment. Furthermore, we illustrated a practical case study to evaluate a suitable optimal option by considering our proposed approaches and analyzed the performance of our currently derived approaches by comparing the results of existing methodologies.

Automated summary

In this article, the concept of power operator is introduced to mitigate the influence of negative information on the decision-making process. The power aggregation tools are robust mathematical operators that facilitate mutual support among input arguments in decision-making. Frank aggregation expressions are reliable and updated versions of triangular norms used for handling complex information. Picture fuzzy set (PFS) is an extended version of fuzzy sets and intuitionistic fuzzy sets, with four terms representing an object's positive grade, abstained grade, negative grade, and refusal grade. New methodologies based on Frank aggregation tools for PF information, such as picture fuzzy frank power average (PFFPA) and picture fuzzy frank power geometric (PFFPG) operators, are proposed. The reliability and performance of these approaches are illustrated through a multi-attribute group decision-making (MAGDM) technique and a case study.