Belief Decision Matrix

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:

    “In politics people throw themselves, as on a sickbed, from one side to the other in the belief they will lie more comfortably.”
    —Johann Wolfgang Von Goethe (1749–1832)

    “How could a man be satisfied with a decision between such alternatives and under such circumstances? No more than he can be satisfied with his hat, which he’s chosen from among such shapes as the resources of the age offer him, wearing it at best with a resignation which is chiefly supported by comparison.”
    —George Eliot [Mary Ann (or Marian)

    “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)