Picture fuzzy aggregation approach with application to third-party logistic provider selection process

Picture fuzzy sets (PFSs) are frequently composed of positive, neutral, and negative memberships and have the benefit of precisely capturing the preferences of decision makers (DMs). This paper introduces innovative picture fuzzy aggregation operators (AOs) based on fundamental operations, which have a number of advantages when dealing with real-world scenarios. Unpredictability and fuzziness coexist in decision-making analysis due to the complexity of the decision-making environment. ”Picture fuzzy numbers” (PFNs) outperform ”intuitionistic fuzzy numbers” (IFNs) when dealing with unclear input. This study proposes two aggregation operators (AOs): ”picture fuzzy hybrid weighted arithmetic geometric aggregation (PFHWAGA) operator” and ”picture fuzzy hybrid ordered weighted arithmetic geometric aggregation (PFHOWAGA) operator.” The proposed operators outperform the current PFN-defined operators. The proposed operator is utilised in the multi-criteria decision-making (MCDM) process to third-party logistic provider selection.