Researchers at the Universidad Politécnica de Madrid’s School of Computing have developed a system to improve decision-making processes concerning complex situations. The system was tested on a real case: the restoration of Lake Svyatoye in Belarus contaminated in the aftermath of the Chernobyl accident.
In their research, professors Antonio Jiménez, Alfonso Mateos and Sixto Rios, of the Decision Analysis and Statistics Group, belonging to the UPM School of Computing’s Department of Artificial Intelligence, proposed to take into account incomplete information and its possible impacts on decision making.
Complex problem solving
Real decision-making problems are usually complex in that several conflicting objectives have to be taken into account simultaneously. In this case, the closer you get to achieving one objective, the worse the prospects of attaining another are. Therefore, there has to be a trade-off between the attainment of objectives.
Multi-Attribute Utility Theory is an approach used widely by academics and practitioners to solve this type of problems. According to this theory, after building a hierarchy of objectives and identifying a set of alternatives and each alternative’s value for or impact on the objectives or criteria under consideration, the decision maker’s preferences have to be quantified.
First, we need to find out the decision maker’s preferences for the possible values or impacts on each criterion under consideration. To do this, a function is defined assigning a utility ranging from 0 (associated with the least preferred impact) to 1 (associated with the most preferred impact) to all the values in the criterion range. Given the impact of an alternative on a criterion, this function tells us what preference the decision maker has for that impact (through its utility value).
Second, we also need to find out the relative importance of the decision-making criteria. In this respect, several methods have been proposed for calculating weights representing this factor.
The elicited decision maker’s preferences are combined with the impacts of the different alternatives on the different attributes in an evaluation function. This function is used to identify the best alternative. Several model evaluation functions, including the additive and the multiplicative models, have been proposed.
Using incomplete information
The School of Computing researchers weighed up the possibility of adding incomplete information on the impacts of some alternatives to the analysis, that is, when the impacts of some alternatives and attributes are not known.
This can be a consequence of several factors. First, some criteria might be intangible or non-monetary because they reflect social or environmental impacts. Second, the alternatives could have random impacts on the criteria because they depend on variables whose values are unknown at the time of decision making. Finally, the available information might be incomplete, not credible or contradictory.
Two approaches for dealing with incomplete information were analysed. The first was to redistribute criteria weights with missing values or impacts logically throughout the objectives hierarchy and across the other criteria. This way, the criteria hierarchy and its assigned weights vary when each alternative is analysed depending on the criteria with missing values.
The second approach to incomplete information analysed was to associate the criterion range (set of possible values) as the impact for a criterion with missing values, assuming that they have a uniform distribution, that is, all the values in the range are considered possible and equally likely.
The best option
Throughout the article, the researchers demonstrate that the best option is the second approach using criteria ranges for unknown impacts, whereas weight redistribution has serious drawbacks.
The analysis is illustrated by a complex real decision-making problem, the restoration of an aquatic ecosystem, Lake Savyatoye (Belarus), unbalanced by radioactive fall-out. The lake was polluted after the accident at the Chernobyl nuclear power plant, and the environmental impact was considered one of the key objectives of the decision-making analysis.
- Jimenez et al. Missing consequences in multiattribute utility theory. Omega, 2009; 37 (2): 395 DOI: 10.1016/j.omega.2007.04.003
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