Multiple attribute group decision making based on multigranulation probabilistic models, MULTIMOORA and TPOP in incomplete q-rung orthopair fuzzy information systems

The concept of q-rung orthopair fuzzy sets (q-ROFSs) severs as an extended form of orthopair fuzzy sets, which excels in flexibly depicting imprecise information existed in multiple attribute group decision making (MAGDM) via allowing a greater space in terms of membership degrees (MD) and non-membership degrees (ND). Moreover, incomplete information systems play a significant role in depicting incomplete information existed in MAGDM. In this paper, for the sake of exploring MAGDM with imprecise and incomplete information, a new MAGDM method based on multigranulation probabilistic models, MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and the technique of precise order preference (TPOP) method in incomplete q-rung orthopair fuzzy (q-ROF) information systems is systematically investigated. First, the concept of multigranulation (MG) incomplete q-ROF information systems is established. Then, a completion technique is put forward to obtain MG q-ROF information systems via patching lost values. Moreover, three versions of MG q-ROF probabilistic rough sets (PRSs) are put forward in light of MG q-ROF information systems. Afterwards, a new MAGDM method is constructed by means of MG q-ROF PRSs, MULTIMOORA and the TPOP method. At last, two experimental studies from open datasets are performed to present the applicability of the constructed MAGDM method, and corresponding sensitivity analysis and comparative analysis are further conducted to demonstrate the validity of the presented methodology.