Antonio Jiménez

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-PLUS: A decision support system for the management of complex fresh water ecosystems contaminated by radionuclides and heavy metals

The accidental release of radioactive substances into the environment leads to the necessity of applying suitable countermeasures for the restoration of the polluted environment. However, despite their obvious benefits, such interventions may result in detrimental effects of an economic, ecological and social nature that must be carefully evaluated. MOIRA-PLUS is a PC-based user-friendly, computerised decision support system (DSS) that helps decision makers to choose optimal countermeasure strategies for different kinds of aquatic ecosystems and contamination scenarios. The DSS MOIRA-PLUS is based on:(a)Validated models to evaluate the behaviour of radionuclides in contaminated water bodies and biota and to assess the effect of countermeasures on contamination levels; (b)Models to assess the radiation dose to people and biota (fish) by relevant exposure pathways, the effect of countermeasures, and the associated economic impact; (c)A multi-attribute analysis (MAA) module to evaluate the effectiveness of different countermeasure strategies by accounting for the social, ecological and economic detriments and costs in relation to their benefits; (d)A software system consisting of: (1) software realisation of the mathematical models; (2) a Geographic Information System (GIS) and associated databases to select the aquatic system of interest and, if necessary, the default environmental data required to run the models; (3) a graphical user interface (GUI); (4) an operating system connecting all the above parts. The flexible structures of the environmental models implemented in MOIRA-PLUS DSS give the potential for the application of these models to several other types of pollutants, such as heavy metals. The DSS can be applied to complex water systems comprising lakes, reservoirs and rivers. In this paper, the main principles underpinning the functioning of the DSS MOIRA-PLUS are described and discussed.

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.

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.

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.

Ranking Methods Based on Dominance Measures Accounting for Imprecision

The additive multi-attribute utility model is widely used in multicriteria decision-making. However, it is often not easy to elicit precise values for the scaling weights representing the relative importance of criteria. In a group decision-making context a very widespread approach is to derive incomplete information, such as weight intervals or ordinal information rather than precise weights from a negotiation process. Different approaches have been proposed to deal with such situations. We advance two approaches based on dominance measures accounting for imprecise weights and compare them with other existing approaches using Monte Carlo simulation.

A Trapezoidal Fuzzy Numbers-Based Approach for Aggregating Group Preferences and Ranking Decision Alternatives in MCDM

In this paper we introduce an approach for solving multiattribute decision-making problems in which there are several decision-makers who individually and independently elicit their preferences. The preferences of each decision-maker are imprecise and represented by an imprecise additive multi-attribute utility function. We allow for incomplete information on the component utility functions and weights assessment, which leads to classes of utility functions and weight intervals, respectively. On the basis of this information, we introduce an approach for calculating the decision-maker group preferences using trapezoidal fuzzy numbers. The method consists of assigning trapezoidal fuzzy numbers to weights and component utilities and then, using an additive utility function to perform the evaluation process. The alternatives are then ranked by the trapezoidal fuzzy numbers representing them and the distances to some preset targets, i.e. the crisp maximum and minimum.

Contracting cleaning services in a European public underground transportation company with the aid of a DSS

This paper deals with the selection of a supplier for cleaning services in a European public underground transportation company as established in the European Community directives, where several conflicting criteria, such as improving service levels and reducing total service costs, must be taken into account simultaneously. The problem is analyzed in depth using the decision analysis methodology, and a decision support system, the Generic Multi-Attribute Analysis system, is used to allay the operational difficulties involved. This system can deal with incomplete information about decision-maker preferences, accounts for uncertainty about offer performance, and uses so-called decision-making with partial information to identify the best offer, taking advantage of imprecise inputs.