Comparison of Evidential Reasoning Algorithm with Linear Combination in Decision Making

Evidential reasoning (ER) approach is a representative method for analyzing uncertain multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problems. Its core is ER algorithm used to combine belief distributions on criteria, which is developed based on Dempster's rule of combination and probability theory. The ER algorithm is nonlinear and more computationally complex than linear combination of belief distributions. To address the necessity of the ER algorithm in MCDM and MCGDM, it is compared with linear combination from three perspectives by simulation. The first is to examine differences between the aggregated assessments derived from the ER algorithm and linear combination. The second is to examine error rates of best alternatives derived from two combination ways. The third is to examine alternative ranking differences derived from two combination ways. To facilitate the comparison, difference between aggregated assessments is designed and score function of alternative is developed from the expected utilities of alternative. Simulation experiments show that differences between the aggregated assessments are influenced by the number of assessment grades, and error rates of best alternatives and alternative ranking differences are influenced by the numbers of criteria and alternatives.