The value/utility function approaches for an individual decision maker involve two elements: (1) the single attribute utility (value) function is used to transform the attribute levels into an interval-value (interval-utility) scale, and (2) the trade-off analysis for defining the weights (scaling constants) is employed to determine the relative importance of the attributes. By multiplying the utilities by the weights, the trade-offs among the attribute utilities are taken into account in the multiattribute utility function. The overall utility or value for alternative i is a weighted average of the single attribute utilities (values). Formally, the value function and utility function models are similar to the weighted linear combination method, except that the score for alternative i with respect to attribute j is replaced with by a value/utility derived from the value or utility function, respectively.
Provided that the conditions are appropriate, the multiattribute value/utility function can be expressed in the form of single value/utility functions. The procedure for the value (utility) function approach involves the following steps:
1. Determine the set of attributes (attribute map layers) and the set of feasible alternatives.
2. Estimate the value (utility) function for each attribute (see "value/utility function approach in estimating weights") and use the function to conert the row data to the value (utility) score map layer.
3. Derive the scaling constants or weights for the attributes (see "trade-off analysis”".
4. Construct the weighted value (utility) map layers; that is, multiply the weights of importance by the value (utility) map layers.
5. Combine the weighted value (utility) maps by summing the weighted value (utility) map layers.
6. Rank the alternatives according to the aggregate value (utility); the alternative with the highest value (utility) is the best alternative.
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