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AbstractA self‐reflecting signed order is a preference relation that compares relative likes and dislikes for items in a set X by jointly ordering X and a disjoint copy of X. If you would like Jones but not Smith appointed to a committee, and also think it more important to exclude Smith than include Jones, your self‐reflecting signed order records this information. We review basic representational theory for signed orders, then examine them when X is multiattributed. Axioms for additive measurement of multiattribute self‐reflecting signed orders are specified for several X‐structures.

Health status is inherently a multiattribute construct. We examine multiattribute utility decompositions for the quality-adjusted life year (QALY) utility model commonly employed in medical decision and cost-effectiveness analyses. We consider several independence conditions on preference, including the classical notions of preferential independence and utility independence, as well as new related notions of standard-gamble independence and time-tradeoff independence. The latter conditions are helpful in simplifying standard-gamble utility assessment procedures and time-tradeoff assessment procedures in the presence of multiple health attributes. Under the QALY model, all these conditions are equivalent and result in a purely multiplicative decomposition of utility over health states.

This paper introduces the notion of a multiattribute utility tree. This graphical representation decomposes the von Neumann–Morgenstern utility of a multiattribute consequence into a sum of products of indifference probability assessments of binary gambles. The utility tree displays the sequence of gambles required to elicit the utility value of a consequence. In addition, it enables the analyst to conduct consistency checks on the indifference assessments provided by the decision maker and to change the order of the assessments based on her comfort level. Once the indifference assessments are provided, the utility value of a consequence can be obtained by direct rollback analysis. On a continuous domain, the utility tree decomposes the functional form of a multiattribute utility function into a sum of products of normalized conditional utility functions. Each attribute in the expansion is conditioned on the boundary values of the attributes expanded before it. This formulation provides a general method for deriving the functional form of a multiattribute utility function under a wide variety of conditions. It also leads to several new independence concepts such as "boundary independence," which is a weaker condition than utility independence, and "corner independence," which makes higher-order independence assertions. Reversing the order of the nodes in the tree relates several widely used notions of utility independence found in the literature.

Many of the complex problems faced by decision makers involve uncertainty as well as multiple conflicting objectives. This book provides a complete understanding of the types of objective functions that should be used in multiattribute decision making. By using tools such as preference, value, and utility functions, readers will learn state-of-the-art methods to analyze prospects to guide decision making and will develop a process that guarantees a defensible analysis to rationalize choices. Summarizing and distilling classical techniques and providing extensive coverage of recent advances in the field, the author offers practical guidance on how to make good decisions in the face of uncertainty. This text will appeal to graduate students and practitioners alike in systems engineering, operations research, business, management, government, climate change, energy, and healthcare

We describe a search problem in which a decision maker (DM) must select among sequentially encountered options. Each option is described by multiple attributes, and the value of an option is given by a separable function of its attribute values. However, the attribute values are not known with certainty, and can only be ascertained in a predefined order, at some fixed cost. During the search the DM can choose to select an option, purchase information about an attribute value, reject (permanently) the current option and continue the search, or terminate the search and accept a status quo outcome. We introduce a threshold policy for this search process, and prove the optimality of this policy for separable value functions. We then furnish a dynamic programming procedure for prescribing an optimal policy for this problem. Finally, we derive analytic solutions to some special cases of the problem, and present a case study that demonstrates a possible use of the proposed approach.

Radiation protection authorities have seen a potential for applying multiattribute risk analysis in nuclear emergency management and planning to deal with conflicting objectives, different parties involved, and uncertainties. This type of approach is expected to help in the following areas: to ensure that all relevant attributes are considered in decision making; to enhance communication between the concerned parties, including the public; and to provide a method for explicitly including risk analysis in the process. A multiattribute utility theory analysis was used to select a strategy for protecting the population after a simulated nuclear accident. The value‐focused approach and the use of a neutral facilitator were identified as being useful.

AbstractAn adaptive approach for modelling individual‐level choice among multiattribute alternatives using the binary logit model is presented. The algorithm involves the collection of paired comparison data. In an effort to maximize the amount of information obtainable from each response, it is based on the experimental design criterion of D‐optimality. A simulation study indicates that the proposed algorithm outperforms other sequential selection approaches in terms of estimation accuracy and predictive efficiency under certain circumstances. The results appear to encourage the use of such an adaptive algorithm for individual‐level modelling in light of the potential reduction in data requirements without significant loss in predictive accuracy.

The construction of a representative multiattribute utility function is important in decision analysis. Existing methods focus mainly on constructions of utility functions on the whole domain of attributes. In some cases, decision makers may provide partial information on their local utility assessments. Therefore, it is a challenging and interesting task to construct utility functions that are compatible with local assessments provided by decision makers. This paper proposes the patchwork construction to accomplish this task. We first define a special local preference structure, the local utility independence and then discuss the patchwork construction that unifies local utility independence on different local domains. The utility function elicited by the patchwork approach under the local utility independence condition is named as the local-utility-independent utility function. Three types of local-utility-independent utility functions on three typical partitions are proposed. These local-utility-independent utility functions have concise and tractable functional forms and indicate intuitive preference structures while matching prior known local utility assessments. Furthermore, the preference structures implied by these three types of local-utility-independent utility functions have a close relationship with the n-switch independence. Sufficient and necessary conditions guaranteeing these local-utility-independent utility functions to indicate n-switch independence are provided, respectively. All three types of local-utility-independent utility functions also have an important application in the approximations of arbitrary utility functions when only some local assessments are provided. As approximations, they are robust and have high accuracy.