Similar to decision matrix, a belief decision matrix is used to describe a multiple criteria decision analysis (MCDA) 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 problem has M rows and N columns or M X N elements, as shown in the following table. Instead of being a single numerical value or a single grade as in a decision matrix, each element in a belief decision matrix is a belief structure.
For example, suppose Alternative i is "Car i", Criterion j is "Engine Quality" assessed by five grades {Excellent, Good, Average, Below Average, Poor}, and "Car i" is assessed to be “Excellent” on "Engine Quality" with a high degree of belief (i.g. 0.6) due to its low fuel consumption, low vibration and high responsiveness. At the same time, the quality is also assessed to be only “Good” with a lower degree of belief (i.g. 0.4 or less) because its quietness and starting can still be improved. If this is the case, then we have Xij={ (Excellent, 0.6), (Good, 0.4)}, or Xij={ (Excellent, 0.6), (Good, 0.4), (Average, 0), (Below Average, 0), (Poor, 0)}.
A conventional decision matrix is a special case of belief decision matrix when only one belief degree in a belief structure is 1 and the others are 0.
Criterion 1 | Criterion 2 | ... | Criterion N | |
---|---|---|---|---|
Alternative 1 | x11 | x12 | ... | x1N |
Alternative 2 | x21 | x22 | ... | x2N |
... | ... | ... | Xij={ (Excellent, 0.6), (Good, 0.4)} | ... |
Alternative M | xM1 | xM2 | ... | xMN |
Famous quotes containing the words belief, decision and/or matrix:
“A belief which leaves no place for doubt is not a belief; it is a superstition.”
—José Bergamín (18951983)
“Because of these convictions, I made a personal decision in the 1964 Presidential campaign to make education a fundamental issue and to put it high on the nations agenda. I proposed to act on my belief that regardless of a familys financial condition, education should be available to every child in the United Statesas much education as he could absorb.”
—Lyndon Baines Johnson (19081973)
“In all cultures, the family imprints its members with selfhood. Human experience of identity has two elements; a sense of belonging and a sense of being separate. The laboratory in which these ingredients are mixed and dispensed is the family, the matrix of identity.”
—Salvador Minuchin (20th century)