Consensus based sustainable decision making using probability hesitant fuzzy preference relations with application on risk assessment in food industry.

This paper describes a consensus-based approach for dealing with multi-person decision-making problems which incorporate probability hesitant fuzzy preference relations. The procedure begins with establishing expected fuzzy preference relations based on the delivered hesitant fuzzy preference relations using a probabilistic aggregation approach, providing the platform for the framework to make decisions. Then, a multiplicative transitive closure formula is defined to construct multiplicative consistent expected fuzzy preference relations and symmetrical matrices, ensuring the reliability of the preference relations. Following that, a consistency analysis is undertaken to assess the consistency levels of the information provided by experts, allowing them to be assigned information priority weights while also guaranteeing that their inputs are balanced and reliable. In order to make sure that all pertinent factors are taken into account during the decision-making process, the ultimate priority weights for the experts are determined through the combination of consistency-based weights with any specified priority weights, if applicable. The consensus process eventually decides whether to aggregate the data and choose the optimal option based on the collective inputs. To strengthen the experts' consensus measure, an enhancement method is provided that detects weak viewpoints in cases of poor consensus and allows for targeted modifications. To highlight the suggested scheme's practicality and usefulness, a comparison example is provided, with results indicating that the method provides valuable insights into the multi-person decision-making process, making it a potential option for achieving agreement in complicated decision-making settings.