A New Approach to Three Way Decision Through Spherical Double Hierarchy Linguistic Information

Branded apps offer both an essential tool for businesses and consumers to interact in real-time and share marketing messages as well as an innovative approach to business that promotes value co-creation. In order to explore the impact of branded apps on customers, this study provides a Three-way decision (TWDs) technique with decision-theoretic rough sets (DTRSs) for selecting branded apps under spherical double hierarchy linguistic term sets (SDHLTSs) information. SDHLTS is a combination of the first hierarchy linguistic term and the second hierarchy linguistic term that can more flexibly describe ambiguity and uncertainty in decision-making (DM) problems. To aggregate the SDHLTSs, we propose a series of aggregation operators and fundamental operational laws for SDHLTSs. A grey relational analysis is considered to evaluate a conditional probability, which improves decision-making. A step-wise algorithm of the TWDs method based on decision-theoretic rough sets (DTRSs) is given for SDHLTSs. Further, a proposed aggregation operator is used to compute the loss function, and the decision’s results are decided by the minimum-loss principle. Finally, a real-world case study of the brand experience of a branded app is considered to demonstrate the efficiency of the proposed methods.