The optimized picture fuzzy weighted geometric operator for decision-making processes and its applications to ambient air pollution

The aggregation operator is a popular tool for dealing with multi-criteria decision-making (MCDM) problems. An MCDM technique based on the optimized picture fuzzy weighted geometric operator (OPFWGO) is proposed in this article. First, the drawbacks of various existing picture fuzzy-weighted geometric aggregation operators (PFWGOs) that lead to imprecise outcomes in some exceptional instances are investigated. Second, an OPFWGO is proposed to address the shortcomings of existing PFWGOs. Furthermore, the suggested OPFWGO’s properties such as idempotency, boundedness, monotonicity, and commutativity are explored. Numerical examples demonstrate that our proposed operator and corresponding MCDM approach are efficient and reasonable enough to prevent ambiguous results in exceptional instances. Finally, we applied the proposed method to rank the World Health Organization regions for air pollution control.