Entropy of the weights given to the Ordered Weighted Average operator (OWA)
The Ordered Weighted Averaging operators, commonly called OWA operators, provide a parameterized class of mean type aggregation operators. OWA was defined by R.R. Yager in 1988. The main characteristic of this aggregation operator is the fact that the weights are associated to the values instead to criteria. In this way, we can define different aggregation policies according to the importance that we associate to high and low performance scores. There exist different measures to characterise a set of weights associated to an OWA operator. In this module we implement the ENTROPY measure.
(For outputs, see below)
A list of criteria. Criteria are always active.
The weights are associated to the values of the alteranatives. Assuming that the values on the alternative will be sorted from the best to the worst (e.g. 7, 5, 5, 3, 1), the list of weights must be ordered according to the importance that is given to the values, from the highest to the lowest. For example a list of weights as (0.5, 0.5, 0, 0, 0) is ignoring the 3 lowest values, and making an average of the two highest ones. A list like (0, 0, 1, 0 ,0 ) is calculating the median, while (0, 0, 0, 0, 1) is taking the minimum. Notice that the sum of weights is required to be 1.
<alternativesValues> <alternativeValue> <values> <value> <real>[...]</real> </value> <value> <integer>[...]</integer> </value> [...] </alternativeValue> </alternativesValues>
Result obtained from the analysis of the OWA weights.
A status message.
For further technical details on the web service underlying this program, have a look at its documentation here.