Description Usage Arguments Details Value References Examples
This function is used as the second step in
weight.differenceToIdeal
for calculating a decision weight for
each attr
in the decision matrix. The methodology of the
'objective approach' for determining the weights is given by references [1]
and [2]. See Details.
1 | differenceToIdeal(normalizedMatrix, attr)
|
normalizedMatrix |
a numeric matrix. If indeed normalized it should only
contain values between |
attr |
attributes IDs, vector of integer numbers corresponding to the attributes you desire to use; attr are assumed to be 1-indexed. Here it represents the number of columns of the input matrix. |
The sum of the output of this functions should always equal 1.
It measures the distance of each column value against the best value for a given attribute. A smaller difference should mean that for that attribute a high value was consistently taking in consideration, thus resulting in a higher weight. Two unintended consequences are: 1. matrices with one row will result in the same weight for all columns and 2. for an attribute where the value does not change at all (even if it's a low value) the function will reward it somewhat disproportionately.
a decision weight (numeric vector with a sum of 1)
[1]Ma, J., Fan, Z. P., & Huang, L. H. (1999). A subjective and objective integrated approach to determine attribute weights. European journal of operational research, 112(2), 397-404.
[2] Fan, Z. P. (1996). Complicated multiple attribute decision making: theory and applications (Doctoral dissertation, Ph. D. Dissertation, North-eastern University, Shenyang, PRC).
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