Incomplete three-way multi-attribute group decision making based on adjustable multigranulation Pythagorean fuzzy probabilistic rough sets

Different from the traditional two-way decision paradigm, three-way decisions (3WD) have been extensively explored in addressing realistic multi-attribute decision making (MADM) by virtue of its powerful performances in minimizing decision risks with the added non-commitment option. Since existing 3WD models can not efficiently handle MADM issues in the group setting with incomplete high-order fuzzy information systems (ISs), the current paper focuses on exploring viable three-way multi-attribute group decision making (MAGDM) methods in light of the multi-granularity 3WD paradigm under incomplete Pythagorean fuzzy (PF) environments. First, the notion of Multigranulation (MG) incomplete PF ISs is constructed. Then, optimistic, pessimistic and adjustable MG PF probabilistic rough sets (PRSs) are proposed after patching lost values. Afterwards, the decision-making-driven 3WD method is extended via adjustable MG PF PRSs, and an improved technique for order preference by similarity to ideal solution (TOPSIS) method with entropy weights is utilized for optimal granularity selections. According to adjustable MG PF PRSs and the improved TOPSIS method, a new three-way MAGDM method is eventually established. At last, two case studies are investigated in the background of mine ventilator fault diagnosis (MVFD) and air quality evaluations (AQE), and several comparative experiments and sensitivity analysis are performed for presenting the effectiveness of the constructed theoretical methodology. (C) 2022 Elsevier Inc. All rights reserved.