A multi-strategy three-way decision approach for tri-state risk loss under q-rung orthopair fuzzy environment

Addressing the decision-making challenge arising from the uncertainty of human cognition, three-way decision (3WD) and q-rung orthopair fuzzy sets (q-ROFSs) are integrated in this paper to propose a multi-strategy three-way decision approach (MS3WDA) for tri-state risk loss (TSRL) under q-rung orthopair fuzzy environment. Based on the ternary thinking of human cognition, the risk loss with hesitation state is considered and constructed under q-rung orthopair fuzzy environment. The TSRL with hesitation state is further constructed by combining the q-rung orthopair fuzzy (q-ROF) information. The conditional probability adopted by the original object classes is improved and extended by the three components of q-ROFSs. Next, the TSRL with q-ROF information and three components of q-ROFSs are integrated with decision-theoretic rough sets (DTRSs) to establish a novel 3WD model. Some relevant properties are also analyzed and discussed for the developed 3WD model. Then, its multi-strategy decision method is proposed based on the multi-strategy perspective. The related strategies with five different levels are designed by considering three different risk appetite perspectives and four different aspects of q-ROF information. The relevant threshold theorems are also given and proved to further provide the theoretical support for our MS3WDA. According to the five different strategies, we further derive the corresponding decision rules of MS3WDA. The key steps and specific algorithm are summarized for MS3WDA. Finally, a case study is provided to demonstrate the practicability and feasibility of MS3WDA. Meanwhile, the rationality, robustness and superiority of MS3WDA are further validated by the sensitivity analysis and comparative analysis.