A new decision-theoretic rough set model with q-rung orthopair fuzzy information

Stock investment is characterized by high risk and massive profit, so it is necessary to propose a scientific and accurate stock assessment and selection method for avoiding investment risks and obtaining high returns. Stock investment evaluation and selection can be regarded as a three-way decision (3WD) problem. Decision-theoretic rough sets (DTRSs) are an excellent tool to cope with 3WDs under risks and uncertainty. Due to the increasing complexity and high uncertainty of decision environments, the loss functions involved in DTRSs are not always expressed with real numbers. As a novel generalized form of Pythagorean fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs), q-rung orthopair fuzzy sets (q-ROFSs) depict uncertain information more widely and flexibly. Thus, it is a significant innovation to combine q-ROFSs with DTRSs and construct a new 3WD model for stock investment evaluation. More specifically, we first extend q-rung orthopair fuzzy numbers (q-ROFNs) to DTRSs, which can offer a novel illustration for loss functions. Then, we establish a novel q-rung orthopair fuzzy DTRS (q-ROFDTRS) model and explore some fundamental properties of the expected losses. Additionally, we propose two methods to handle q-ROFNs and obtain 3WDs. These two methods are compared, and their characteristics and applicability are analysed. Finally, a practical case concerning stock investment evaluation is supplied to illustrate the effectiveness and the superiority of the developed approaches over existing methods.