LAUSR

Picture fuzzy sets (PFSs) are one of the fundamental concepts for addressing uncertainties in decision problems, and they can address more uncertainties compared to the existing structures of fuzzy sets; thus, their implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the decision-maker over the multiple parameters. Taking this feature and the significances of the PFSs into consideration, the main objective of the article is to describe some reliable sine trigonometric laws for PFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the picture fuzzy numbers. Also, we characterized the desirable properties of the proposed operators. Then, we presented a group decision-making strategy to address the multiple attribute group decision-making (MAGDM) problem using the developed aggregation operators and demonstrated this with a practical example. To show the superiority and the validity of the proposed aggregation operations, we compared them with the existing methods and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.