A novel model for multi-criteria assessment based on BWM and possibilistic chance-constrained programming

Abstract

The best-worst method (BWM) is one of the most important methods for determining the weights of criteria or options in multi-criteria decision-making (MCDM) and has attracted the attention of many researchers due to its advantages such as fewer numbers of comparisons and higher consistency rate. Given that real-world decision making is often associated with uncertainty, in this study several fuzzy linear programming models have been developed using trapezoidal fuzzy numbers for BWM that can calculate the optimal weights of criteria. The proposed models are based on three measures of possibility, necessity, and credibility, which are parts of possibilistic chance-constrained programming (PCCP). Development of BWM based on possibilistic distribution allows the decision-maker (DM) to take into account uncertainties in the calculation of weights as well as include his optimistic, pessimistic, and intermediate attitudes in determining the weight of decision criteria. The possibility approach reflects the DM's optimistic view of the issue. The necessity approach is used in situations where the DM prefers a pessimistic view, and the credibility approach indicates that DM has an intermediate view between optimistic and pessimistic views, or in other words, considers an intermediate approach between possibility and necessity approaches. Finally, the feasibility and effectiveness of the proposed approaches were tested using two numerical examples and the sensitivity of the results was analyzed for different values of uncertainty (alpha parameter). Also, by analyzing the coefficient of variation, it was found that the results of the proposed models had very little dispersion for different values of uncertainty, and this confirmed the validity of the results. Examining the results of the proposed models revealed that the possibility approach provides more robust results than other approaches when the levels of confidence of the decision-makers are changed.