Belief structure
A belief structure is a distributed assessment with beliefs.
A belief structure is used in the evidential reasoning (ER) approach for multiple-criteria decision analysis (MCDA) to represent the performance of an alternative option on a criterion.
In the ER approach, an MCDA problem is modelled by a belief decision matrix instead of a conventional decision matrix. The difference between the two is that, in the former, each element is a belief structure; in the latter, conversely, each element is a single value.
Application
For example, the quality of a car engine may be assessed to be “excellent” with a high degree of belief due to its low fuel consumption, low vibration and high responsiveness. At the same time, the quality may be assessed to be only “good” with a lower degree of belief because its quietness and starting can still be improved. Such an assessment can be modeled by a belief structure: Si=, where Si stands for the assessment of engine on the ith criterion. In the belief structure, “excellent” and “good” are assessment standards, whilst “0.6” and “0.4” are degrees of belief.