Regret-based domination three-way decision-making model with circular spherical fuzzy Mahalanobis distance

This article proposes a revolutionary three-way multi-attribute model in response to the increased complexity and risk in decision-making processes. This model combines three-way decision rules with the influential behavioral theories of regret and prospect. To address uncertainties in evaluation data, a circular spherical fuzzy set is seamlessly integrated into the information system, noting that this method can also be smoothly applied to disc spherical fuzzy sets (D-SFSs). Moreover, a pioneering method utilizing correlation coefficients and variances is introduced for attribute weighting. The conventional Mahalanobis distance is extended to a circular, spherical, fuzzy Mahalanobis distance. A novel approach is developed to estimate conditional probabilities based on the distinct regret-based dominating and rejoice-based dominating relations in circular spherical fuzzy sets (C-SFSs). Additionally, three scoring systems based on prospect theory yield despondent, expectant, and balanced decision-making strategies and provide priceless insights into various decision-maker mindsets. Furthermore, to illustrate the practical application of these methods with D-SFSs information, an example has been solved utilizing D-SFSs.