Multi-attribute utility functions

It can be divided in two parties the first involving the elicitation of one dimensional utility function to each risk dimension and the second to the determine the multi-attribute utility function. 

The main method for modelling preferences under uncertainty is the Multi-Attribute Utility Theory (MAUT). In its simples (additive) form, a multi attribute utility function resembles a multi-attribute value function. The way to find parameters of a utility function is however different. While in the case of MAVT the scores and weights can be determined based on direct comparison of consequences, in the case of MAUT these components are found through lottery types of questions (Keeney Raiffa, 1999). 

In order to estimate risks at each section considered, the multi-attribute utility function is combined with the probability density function. For each section of the pipeline established and for each scenario considered accidental, the loss has been defined by equation 2 ... 

According to Brito Almeida (2009), the multiattribute utility function is additive, which implies the independence of preferences among the dimensions. Thus the multi-attribute utility function U (h,ej) is obtained based on one-dimensional utility functions U(h), U(e) and U(f), as described below ... 

Using procedures for elicitation through a process of a structured set of questions, the decision maker makes probabilistic choices of lotteries involving payoffs of the three dimensions (Brito Almeida, 2009). After this process, scale constants were obtained for the multi-attribute utility function, these scale constants are k = 0.45, hi = 0.15 and hi = 0.40. 

Another step of the model includes estimating the risks and ranking them as presented in Table 1. To estimate the risk assigned to each section of the pipeline, the multi-attribute utility function is associated with the probability density function of the consequences. 

G. W. Torrance, W. Furlong, D. Feeny and M. Boyle, Multi-attribute preference functions Health utilities index, PharmacoEconomics 7(6) (1995), 503-520. 

Multi-attribute utility theory, which hes within the concepts of MCDA, enables the values of the DM s preferences to be aggregated (through the utility function) from multiple attributes, together with the uncertainty inherent in their consequences E(c 0, q) and hazard scenarios 7i(0), in a unique synthesis criterion function. 

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