Picture fuzzy soft-max Einstein interactive weighted aggregation operators with applications

This research paper introduces novel aggregation methods known as the picture fuzzy soft-max Einstein interactive weighted average (PiFSMEIWA) and the picture fuzzy soft-max Einstein interactive weighted geometric (PiFSMEIWG) operators. These operators are specifically developed to improve the decision-making process by offering a comprehensive framework for aggregating multiple criteria when selecting sustainable biomass resources for bioenergy production. The PiFSMEIWA operator combines the benefits of the soft-max function and Einstein interactive operations to create an all-encompassing framework for information aggregation. Conversely, the PiFSMEIWG operator broadens the capabilities of PiFSMEIWA by integrating weighted geometric aggregation through the soft-max function, effectively managing uncertain and imprecise information while considering the decision maker's (DM's) preferences. To exemplify the practical application of these operators, a case study concentrating on the selection of sustainable biomass resources for bioenergy production is presented. This case study takes into consideration diverse factors such as biomass availability, environmental impact, economic feasibility, and social acceptance. Through the utilization of the proposed aggregation operators, a picture fuzzy decision-making model is devised to assist in the selection of biomass resources. This model examines various criteria and assesses the suitability of different biomass resources based on their overall performance. The experimental results underscore the efficacy and resilience of the proposed operators and decision-making model in dealing with uncertainty and imprecision. The study's findings offer valuable insights for policymakers, researchers, and stakeholders involved in the selection of biomass resources.