An extended picture fuzzy MULTIMOORA method based on Schweizer–Sklar aggregation operators

The purpose of this paper is to construct an extended picture fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method based on Schweizer–Sklar prioritized aggregation operators and picture fuzzy set. First, based on Schweizer–Sklar t-norm and t-conorm, picture fuzzy Schweizer–Sklar operations involving a variable parameter are defined to make the corresponding operations more flexible than other operations. Second, the picture fuzzy Schweizer–Sklar prioritized aggregation operators, namely the picture fuzzy Schweizer–Sklar prioritized weighted average operator and the picture fuzzy Schweizer–Sklar prioritized weighted geometric operator, are developed, and their related properties are investigated as well. Third, an extended picture fuzzy MULTIMOORA method with unknown weight information, which involves the ratio system, the reference point, and the multiplicative form methods simultaneously, is constructed based on the developed aggregation operators. Finally, an illustrative example with public–private–partnership investment project selection is presented to verify the feasibility and validity of the constructed method. The results indicate that the constructed method is effective to realize an optimal decision-making.