Abstract
This study develops an R-mathematical programming method for multiple attribute group decision-making (MAGDM) problems with assessment values of alternatives and truth degrees of pairwise alternative comparisons represented by R-sets while the decision maker holds subjective bounded rationality. First, a novel scalar multiplication operation and defuzzification of R-sets are proposed to allow the use of R-sets in MAGDM problems. Subsequently, based on prospect theory and R-sets, a new technique is proposed to compute the individual overall prospect value of an alternative by simultaneously considering the positive ideal solution (PIS) and negative ideal solution (NIS). Additionally, the R-group consistency index (R-GCI) and R-group inconsistency index (R-GII) are defined using the individual overall prospect values of alternatives. The decision makers’ weights, attribute weights, PIS, and NIS are estimated by establishing a novel R-mathematical programming model, which is solved by the external archive-based constrained state transition, while the collective overall prospect values are computed to derive the final ranking order of alternatives. Thus, a new R-LINMAP method is developed to solve MAGDM. A practical instance concerning online physician selection is provided with the corresponding sensitive and comparative analyses to verify the applicability, validity, and superiority of the developed method.
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