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:
“To be faced with what so-and-sos mother lets him do, or what the teacher said in class today or what all the kids are wearing is to be required to reexamine some part of our belief structure. Each time we rethink our values we reaffirm them or begin to change them. Seen in this way, parenthood affords us an exceptional opportunity for growth.”
—Ruth Davidson Bell (20th century)
“The women of my mothers generation had, in the main, only one decision to make about their lives: who they would marry. From that, so much else followed: where they would live, in what sort of conditions, whether they would be happy or sad or, so often, a bit of both. There were roles and there were rules.”
—Anna Quindlen (20th century)
“The matrix is God?
In a manner of speaking, although it would be more accurate ... to say that the matrix has a God, since this beings omniscience and omnipotence are assumed to be limited to the matrix.
If it has limits, it isnt omnipotent.
Exactly.... Cyberspace exists, insofar as it can be said to exist, by virtue of human agency.”
—William Gibson (b. 1948)