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:
“There is a place where we are always alone with our own mortality, where we must simply have something greater than ourselves to hold onto—God or history or politics or literature or a belief in the healing power of love, or even righteous anger.... A reason to believe, a way to take the world by the throat and insist that there is more to this life than we have ever imagined.”
—Dorothy Allison (b. 1949)
“Will mankind never learn that policy is not morality,—that it never secures any moral right, but considers merely what is expedient? chooses the available candidate,—who is invariably the devil,—and what right have his constituents to be surprised, because the devil does not behave like an angel of light? What is wanted is men, not of policy, but of probity,—who recognize a higher law than the Constitution, or the decision of the majority.”
—Henry David Thoreau (1817–1862)
“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
—Margaret Atwood (b. 1939)