Belief structure
Encyclopedia
A belief structure is a distributed assessment with beliefs. It is used in the evidential reasoning (ER) approach
for multi-criteria decision analysis to represent the performance of an alternative option on a criterion. For example, the quality of a car engine may be assessed to be “excellent” with a high degree of belief (e.g. 0.6) 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 (e.g. 0.4 or less) because its quietness and starting can still be improved. Such an assessment can be modeled by a belief structure: Si(engine)={(excellent, 0.6), (good, 0.4)}, where Si stands for the assessment of engine on the ith criterion (quality). In the belief structure, “excellent” and “good” are assessment standards, whilst “0.6” and “0.4” are degrees of belief.
In the ER approach, an MCDA problem is modelled by a belief decision matrix
instead of a conventional decision matrix
. The difference of the two is that in the former, each element is a belief structure while in the latter, each element is a single value (either numerical or textual).
The Evidential Reasoning Approach
Decision Matrix
Belief decision matrix
Evidential Reasoning Approach
In decision theory, the evidential reasoning approach , is a generic evidence-based multi-criteria decision analysis approach for dealing with problems having both quantitative and qualitative criteria under various uncertainties including ignorance and randomness...
for multi-criteria decision analysis to represent the performance of an alternative option on a criterion. For example, the quality of a car engine may be assessed to be “excellent” with a high degree of belief (e.g. 0.6) 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 (e.g. 0.4 or less) because its quietness and starting can still be improved. Such an assessment can be modeled by a belief structure: Si(engine)={(excellent, 0.6), (good, 0.4)}, where Si stands for the assessment of engine on the ith criterion (quality). In the belief structure, “excellent” and “good” are assessment standards, whilst “0.6” and “0.4” are degrees of belief.
In the ER approach, an MCDA problem is modelled by a belief decision matrix
Belief decision matrix
Similar to decision matrix, a belief decision matrix is used to describe a multiple criteria decision analysis problem in the Evidential Reasoning Approach. If in an MCDA problem, there are M alternative options and each need to be assessed on N criteria, then the belief decision matrix for the...
instead of a conventional decision matrix
Decision Matrix
A decision matrix is a list of values in rows and columns that allows an ologist to systematically identify, analyze, and rate the performance of relationships between sets of values and information. Elements of a decision matrix show decisions based on certain decision criteria...
. The difference of the two is that in the former, each element is a belief structure while in the latter, each element is a single value (either numerical or textual).
See also
MCDAThe Evidential Reasoning Approach
Evidential Reasoning Approach
In decision theory, the evidential reasoning approach , is a generic evidence-based multi-criteria decision analysis approach for dealing with problems having both quantitative and qualitative criteria under various uncertainties including ignorance and randomness...
Decision Matrix
Decision Matrix
A decision matrix is a list of values in rows and columns that allows an ologist to systematically identify, analyze, and rate the performance of relationships between sets of values and information. Elements of a decision matrix show decisions based on certain decision criteria...
Belief decision matrix
Belief decision matrix
Similar to decision matrix, a belief decision matrix is used to describe a multiple criteria decision analysis problem in the Evidential Reasoning Approach. If in an MCDA problem, there are M alternative options and each need to be assessed on N criteria, then the belief decision matrix for the...