Linguistic Z Number Fuzzy Probabilistic Rough Set and Their Corresponding Three-Way Decisions

The main objective of this chapter is to apply decision-theoretic rough sets (DTRS) to deal with uncertainty and risk in three-way decisions (3WDs) that involve multiple experts with linguistic Z number (LZN) information systems (LZNIS). We begin by presenting an LZN fuzzy probabilistic rough fuzzy set (FPRS) (LZN-FPRS) model that uses LZN information to assess the fuzzy decisive objects of each object in the universe concerning the attribute set. After that, we suggest a DTRS model that employs LZNIS to determine the loss functions (LFs). Next, we establish a 3WDs framework, based on the DTRS model with LZNIS and obtain the relevant decisive rules that reduce the risk. Furthermore, we propose a new decisive model, based on the 3WD framework with DTRSs that uses LZNIS for solving multiple attribute group decision-making (MAGDM) problems. At last, we apply the proposed MAGDM model in corresponding with the optimal selection of public health emergency agencies and show the effectiveness of our proposed method by comparative analysis.