Consistency Simulation and Optimization for HPIBM Model in Emergency Decision Making

Emergencies in ethnic regions in China happened increasingly, and emergency decision making become more complicated than that in other regions since it involves religions, cultures and national customs etc. The data consistency and incompleteness issues are two of the hot research topics in an emergency decision matrix (EDM). The Hadamard product induced bias matrix (HPIBM) model can be used to identify the most inconsistent entry in an EDM. In this paper, we provide experimental consistency simulations for HPIBM by randomly generating decision matrices with orders 3 to 7. In addition, we propose a novel HPIBM for estimating the missing judgments in an EDM by constructing optimization problem while improving the consistency ratio. A numerical example is used to illustrate the proposed method, and the result shows that the proposed method can find the optimal solutions for missing values and help emergency manager make fast response to the emergency incident even there are incomplete decision information.