On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty

In multiple attribute decision analysis (MADA), one often needs to deal with both numerical data and qualitative information with uncertainty. It is essential to properly represent and use uncertain information to conduct rational decision analysis. Based on a multilevel evaluation framework, an evidential reasoning (ER) approach has been developed for supporting such decision analysis, the kernel of which is an ER algorithm developed on the basis of the framework and the evidence combination rule of the Dempster-Shafer (D-S) theory. The approach has been applied to engineering design selection, organizational self-assessment, safety and risk assessment, and supplier assessment. In this paper, the fundamental features of the ER approach are investigated. New schemes for weight normalization and basic probability assignments are proposed. The original ER approach is further developed to enhance the process of aggregating attributes with uncertainty. Utility intervals are proposed to describe the impact of ignorance on decision analysis. Several properties of the new ER approach are explored, which lay the theoretical foundation of the ER approach. A numerical example of a motorcycle evaluation problem is examined using the ER approach. Computation steps and analysis results are provided in order to demonstrate its implementation process.