Breast cancer pre-diagnosis based on incomplete picture fuzzy multi-granularity three-way decisions

PurposeThree-way decision (3WD) and probabilistic rough sets (PRSs) are theoretical tools capable of simulating humans' multi-level and multi-perspective thinking modes in the field of decision-making. They are proposed to assist decision-makers in better managing incomplete or imprecise information under conditions of uncertainty or fuzziness. However, it is easy to cause decision losses and the personal thresholds of decision-makers cannot be taken into account. To solve this problem, this paper combines picture fuzzy (PF) multi-granularity (MG) with 3WD and establishes the notion of PF MG 3WD.Design/methodology/approachAn effective incomplete model based on PF MG 3WD is designed in this paper. First, the form of PF MG incomplete information systems (IISs) is established to reasonably record the uncertain information. On this basis, the PF conditional probability is established by using PF similarity relations, and the concept of adjustable PF MG PRSs is proposed by using the PF conditional probability to fuse data. Then, a comprehensive PF multi-attribute group decision-making (MAGDM) scheme is formed by the adjustable PF MG PRSs and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Finally, an actual breast cancer data set is used to reveal the validity of the constructed method.FindingsThe experimental results confirm the effectiveness of PF MG 3WD in predicting breast cancer. Compared with existing models, PF MG 3WD has better robustness and generalization performance. This is mainly due to the incomplete PF MG 3WD proposed in this paper, which effectively reduces the influence of unreasonable outliers and threshold settings.Originality/valueThe model employs the VIKOR method for optimal granularity selections, which takes into account both group utility maximization and individual regret minimization, while incorporating decision-makers' subjective preferences as well. This ensures that the experiment maintains higher exclusion stability and reliability, enhancing the robustness of the decision results.