The selection of the proper P2P energy trading platform is a complicated multi-attribute decision-making (MADM) dilemma that involves evaluating different alternatives against various attribute. Traditional MADM techniques often fail to capture the bipolarity of certain attribute, where positive and negative aspects are simultaneously present. This duality of attribute therefore requires a more advance method of modeling and decision making (DM). The bipolar fuzzy set (BFS) framework presents a possible research gap-filling solution by enabling the consideration of both positive and negative information associated with each attribute at the same time. This article aims to use BFS to create a MADM technique that will be able to model the bipolarity of the criteria, and provide a structured approach for the selection of the most suitable P2P energy trading platform. Further, this article contains various aggregation operators within BFS based on Aczel-Alsina (AA) t-norm and t-conorm, which play a critical role in the proposed MADM approach. After that, the case study, "Selection of Energy Trading Platform for P2P Energy Trading" is investigated by employing the invented approach. In the end, the advantages and dominance of the inaugurated work over some of the prevailing literature are demonstrated through comparative analysis.