Alfonso Mateos

A decision support system for multiattribute utility evaluation based on imprecise assignments

This paper describes a decision support system based on an additive or multiplicative multiattribute utility model for identifying the optimal strategy. This is intended to allay many of the operational difficulties involved in assessing and using multiattribute utility functions. The system admits imprecise assignments for weights and utilities and uncertainty in the multiattribute strategies, which can be defined in terms of ranges for each attribute instead of single values. Inputs can be subjected to different sensitivity analyses, permitting users to test the robustness of the ranking of the strategies and gain insight into and confidence about the final solution. An application of the system to the restoration of a contaminated lake is illustrated throughout the paper.

Monte Carlo simulation techniques for group decision making with incomplete information

Abstract In this paper we deal with group decision-making problems where several decision makers elicit their own preferences separately. The decision makers’ preferences are quantified using a decision support system, which admits incomplete information concerning the decision makers’ responses to the questions they are asked. Consequently, each decision maker proposes classes of utility functions and attribute weight intervals for the different attributes. We introduce an approach based on Monte Carlo simulation techniques for aggregating decision maker preferences that could be the starting point for a negotiation process, if necessary. The negotiation process would basically involve the decision maker tightening the imprecise component utilities and weights to output more meaningful results and achieve a consensus alternative. We focus on how attribute weights and the component utilities associated with a consequence are randomly generated in the aggregation process taking into account the decision-makers’ preferences, i.e., their respective attribute weight intervals and classes of utility functions. Finally, an application to the evaluation of intervention strategies for restoring a radionuclide contaminated lake illustrates the usefulness and flexibility of this iterative process.

MOIRA: A decision support system for decision making on aquatic ecosystems contaminated by radioactive fallout

Interventions to restore radionuclide contaminated aquatic ecosystems may reduce individual and collective radiation doses, but may also result in detrimental ecological, social and economic effects. Decision makers must carefully evaluate possible impacts before choosing a countermeasure, hence decision analysis methods constitute an important aid to rank intervention strategies after the contamination of an aquatic ecosystem. We describe MOIRA, a decision support system for the identification of optimal remedial strategies to restore water systems after accidental introduction of radioactive substances. MOIRA includes an evaluation module based on a multi-attribute value model to rank alternatives and a module to perform multiparametric sensitivity analyses, both with respect to weights and values, to allow us to gain insights into the problem. The problem is under certainty since the validation of models used to quantify countermeasure impacts suggests little uncertainty in policy effects.The system is implemented in a PC based decision support system which allows the inclusion of all relevant information.

Dominance, potential optimality and alternative ranking in imprecise multi-attribute decision making

In this paper, we introduce a methodology based on an additive multiattribute utility function that does not call for precise estimations of the inputs, such as utilities, attribute weights and performances of decision alternatives. The information about such inputs is assumed to be in the form of ranges, which constitute model constraints and give rise to nonlinear programming problems. This has significant drawbacks for outputting the sets of non-dominated and potentially optimal alternatives for such problems, and we, therefore, propose their transformation into equivalent linear programming problems. The set of non-dominated and potentially optimal alternatives is a non-ranked set and can be very large, which makes the choice of the most preferred alternative very difficult. The above problem is solved by proposing several methods for alternative ranking. An application to the disposal of surplus weapons-grade plutonium is considered, showing the advantages of this approach.

Solving dominance and potential optimality in imprecise multi-attribute additive problems

Abstract We consider the multicriteria decision-making problem where there is partial information on decision maker preferences, represented by means of an imprecise multiattribute additive utility function, and where the consequences of the alternatives or strategies are also possibly imprecise. Under these circumstances we consider how useful problem-solving concepts, namely nondominated, potentially optimal, adjacent potentially optimal alternatives, can be analytically computed. Thus, the problem can be solved much more efficiently using the classical methodology of linear programming.

Postoptimal analysis in a multi-attribute decision model for restoring contaminated aquatic ecosystems

We describe the evaluation module of the MOIRA system, developed to identify optimal remedial strategies for restoring radionuclide contaminated aquatic ecosystems and drainage areas. This module includes a multiparametric sensitivity analysis, which is based on a multi-attribute additive value model, aimed at identifying optimal remedial strategies for restoring aquatic ecosystems contaminated by radionuclides. We introduce the sensitivity analysis to check the robustness of the conclusions on the inputs. This provides insights into the problem in the sense of making better use of the available information. This analysis is focused on judgemental inputs, imprecise value functions on attributes and imprecise scaling factors or weights for their aggregation. These are of utmost importance in determining the optimal countermeasures.

A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawbacks for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature.

Dominance intensity measuring methods in MCDM with ordinal relations regarding weights

We consider a multicriteria decision-making context in which the decision-makers preferences are represented by a multi-attribute additive value function. We account for imprecision concerning the performance of alternatives, value functions and weights, which represent the relative importance of criteria. We propose two new methods based on dominance intensity measures aimed at ranking alternatives. Both methods can be applied to different representations of imprecision about weights. Their performance is compared with other existing approaches when ordinal weight information represents imprecision concerning weights. Monte Carlo simulation is used for the comparison in terms of a hit ratio and a rank-order correlation.

A new dominance intensity method to deal with ordinal information about a DM's preferences within MAVT

Dominance measuring methods are an approach to deal with complex decision-making problems with imprecise information. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in different ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we propose a new dominance measuring method to deal with ordinal information about decision-maker preferences in both weights and component utilities. It takes advantage of the centroid of the polytope delimited by ordinal information and builds triangular fuzzy numbers whose distances to the crisp value 0 constitute the basis for the definition of a dominance intensity measure. Monte Carlo simulation techniques have been used to compare the performance of this method with other existing approaches.

The utility efficient set and its interactive reduction

We assume a decision situation under risk with incomplete information on preferences modelled as a vector utility function. We consider an additive aggregation of its components and partial information on the scaling constants. We develop the concept of utility efficiency to identify efficient strategies in discrete problems when the information about the scaling constants of the decision maker is in the form of a polyhedral cone. A characterization of the utility efficient set provides a practical way to compute such efficient strategies. We then discuss an interactive method based on the assessment of the scaling constants via an interactive paired comparison with its convergence. The method is complemented by a procedure to reduce the utility efficient set to aid in the process of reaching a final strategy.