The expected value decision rule is a probabilistic additive weighting approach to aggregating data on attributes and decision makers’ preferences. It deals with the uncertainties associated with the variability of decision outcomes. This variability can be expressed in terms of the probability distribution associated with alternative decision consequences. The probability distribution may be determined on the basis of data analysis, professional judgments, analytical models, simulation models, or any combination of these methods (see commensurate scale generation methods).
The concept of” expected value” is central to the probabilistic additive weighting decision rules. For each alternative the possible decision outcomes are quantified by the probability distribution. In other words, there is a random variable assigned to each alternative decision. The expected value is a weighted mean (average) of the possible outcomes of a random variable, with the probability outcomes used as weights (the probabilities or weights should not be confused with the weights of importance associated with attributes).
The probabilistic additive weighting model combines the value function approach and the expected value concepts. It is a formal method of combining the probabilities of an preferences for consequences. The higher the expected value, the more desirable is the alternative. The procedure for the value (utility) function approach involves the following steps:
1. Determine the set of feasible alternatives.
2. Estimate the value (utility) function for each attribute (see “commensurate scale generation methods”) and use this function to convert the row data to the value (utility) score map layer.
3. Derive the scaling constant or weights for the attributes.
4. Estimate the probability distributions for each attribute.
5. Generate the expected value maps by multiplying each attribute value level by the corresponding probability map layer and adding the resulting layers.
6. Construct the weighted expected value map layers by multiplying the expected value maps by associated weights determined in step 3.
7. Sum the weighted expected value map layers to obtain the aggregate expected value map layer.
8. Rank the alternative according to the expected outcomes; the alternative with the highest expected value is the best alternative.
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