Evaluation of agriculture-food 4.0 supply chain approaches using Fermatean probabilistic hesitant-fuzzy sets based decision making model

The benchmarking of agri-food 4.0 supply chain (Agri4SC) falls under the multiple criteria problem in supply chain visibility (SCV) and supply chain resource integration (SCRI) for improving data analytics capabilities and achieving sustainable performance (SP). It is considered a multiple criteria decision-making (MCDM) problem due to three main concerns, namely, multiple Agri4SC evaluation criteria including the SCV, SCRI and SP criteria. These criteria have relative importance and trade-offs. Despite the tremendous efforts over the last years, none of the developed Agri4SCs have met all of the essential Agri4SC evaluation criteria. Another concern raised in the evaluation and benchmarking of the Agri4SC is the uncertainty of experts. Thus, the main contribution of this research is to propose an Agri4SC benchmarking framework in SCV and SCRI for improving data analytics capabilities and achieving SP based on an extension of the proposed Fermatean probabilistic hesitant fuzzy sets (FPHFSs) and MCDM methods. The methodology process is divided into six main parts. Firstly, an Agri4SC decision matrix is formulated based on the intersection of the Agri4SC alternatives and criteria to cover multiple Agri4SC evaluation criteria issues. Secondly, novel FPHFSs are proposed along with their operational laws, score function, accuracy function, Fermatean probabilistic hesitant fuzzy average mean operator and Fermatean probabilistic hesitant fuzzy weighted average operator. The FPHFS can encompass more sophisticated and uncertain evaluation information. Thirdly, Fermatean probabilistic hesitant fuzzy weighted zero inconsistency is formulated to assign weights to the evaluation criteria. Fourthly, the Fermatean probabilistic hesitant fuzzy decision by opinion score method (FPH-FDOSM) is formulated and used to score the alternatives that were evaluated subjectively based on SCV criteria. Fifthly, the FPH-FDOSM-based multi attributive ideal-real comparative analysis (MAIRCA) scoring method with equal probabilities is proposed to score Agri4SC alternatives that were evaluated subjectively based on weighted economic, environmental and social factors. Lastly, the MAIRCA ranking method with unequal probabilities is introduced to benchmark Agri4SC alternatives that were evaluated objectively based on the weighted subcriteria of SP and the trade-offs amongst the identified criteria. The robustness and reliability of the results are tested via sensitivity analysis and Spearman's correlation coefficient.