A Combined Weighting Method Based on Hybrid of Interval Evidence Fusion and Random Sampling

Abstract

Due to the complexity of system and lack of expertise, epistemic uncertainties may present in the experts’ judgment on the importance of certain indices during group decision-making. A novel combination weighting method is proposed to solve the index weighting problem when various uncertainties are present in expert comments. Based on the idea of evidence theory, various types of uncertain evaluation information are uniformly expressed through interval evidence structures. Similarity matrix between interval evidences is constructed, and expert’s information is fused. Comment grades are quantified using the interval number, and cumulative probability function for evaluating the importance of indices is constructed based on the fused information. Finally, index weights are obtained by Monte Carlo random sampling. The method can process expert’s information with varying degrees of uncertainties, which possesses good compatibility. Difficulty in effectively fusing high-conflict group decision-making information and large information loss after fusion is avertible. Original expert judgments are retained rather objectively throughout the processing procedure. Cumulative probability function constructing and random sampling processes do not require any human intervention or judgment. It can be implemented by computer programs easily, thus having an apparent advantage in evaluation practices of fairly huge index systems.