Ranking Alternatives on the Basis of the Intensity of Dominance and Fuzzy Logic within MAUT

We introduce dominance measuring methods to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision making problems on the basis of Multi-Attribute Utility Theory (MAUT). We consider the situation where the alternative performances are represented by uniformly distributed intervals, and there exists imprecision concerning the decision-makers¿ preferences, by means of classes of individual utility functions and imprecise weights represented by weight intervals or fuzzy weights, respectively. An additive multi-attribute utility model is used to evaluate the alternatives under consideration, which is considered a valid approach in most practical cases. The approaches we propose are based on the dominance values between pairs of alternatives that can be computed by linear programming, which are then transformed into dominance intensities from which a dominance intensity measure is derived. The methods proposed are compared with other existing dominance measuring methods and other methodologies by Monte Carlo simulation techniques. The performance is analyzed in terms of two measures of efficacy: hit ratio, the proportion of all cases in which the method selects the same best alternative as in the TRUE ranking, and the Rank-order correlation, which represents how similar the overall rank structures of alternatives are in the TRUE ranking and in the ranking derived from the method. The approaches are illustrated with an example consisting on the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides

Dominance Measuring Method Performance under Incomplete Information about Weights.

In multi-attribute utility theory, it is often not easy to elicit precise values for the scaling weights representing the relative importance of criteria. A very widespread approach is to gather incomplete information. A recent approach for dealing with such situations is to use information about each alternative?s intensity of dominance, known as dominance measuring methods. Different dominancemeasuring methods have been proposed, and simulation studies have been carried out to compare these methods with each other and with other approaches but only when ordinal information about weights is available. In this paper, we useMonte Carlo simulation techniques to analyse the performance of and adapt such methods to deal with weight intervals, weights fitting independent normal probability distributions orweights represented by fuzzy numbers.Moreover, dominance measuringmethod performance is also compared with a widely used methodology dealing with incomplete information on weights, the stochastic multicriteria acceptability analysis (SMAA). SMAA is based on exploring the weight space to describe the evaluations that would make each alternative the preferred one

Aproximaciones del conjunto eficiente en decisión multicriterio

El conjunto eficiente en la Teoría de la Decisión Multicriterio juega un papel fundamental en los procesos de solución ya que es en este conjunto donde el decisor debe hacer su elección más preferida. Sin embargo, la generación de tal conjunto puede ser difícil, especialmente en problemas continuos y/o no lineales. El primer capítulo de esta memoria, es introductorio a la Decisión Multicriterio y en él se exponen aquellos conceptos y herramientas que se van a utilizar en desarrollos posteriores. El segundo capítulo estudia los problemas de Toma de Decisiones en ambiente de certidumbre. La herramienta básica y punto de partida es la función de valor vectorial que refleja imprecisión sobre las preferencias del decisor. Se propone una caracterización del conjunto de valor eficiente y diferentes aproximaciones con sus propiedades de encaje y convergencia. Varios algoritmos interactivos de solución complementan los desarrollos teóricos. El tercer capítulo está dedicado al caso de ambiente de incertidumbre. Tiene un desarrollo parcialmente paralelo al anterior y utiliza la función de utilidad vectorial como herramienta de modelización de preferencias del decisor. A partir de la consideración de las distribuciones simples se introduce la eficiencia en utilidad, su caracterización y aproximaciones, que posteriormente se extienden a los casos de distribuciones discretas y continuas. En el cuarto capítulo se estudia el problema en ambiente difuso, aunque de manera introductoria. Concluimos sugiriendo distintos problemas abiertos.---ABSTRACT---The efficient set of a Multicriteria Decicion-Making Problem plays a fundamental role in the solution process since the Decisión Maker's preferred choice should be in this set. However, the computation of that set may be difficult, specially in continuous and/or nonlinear problems. Chapter one introduces Multicriteria Decision-Making. We review basic concepts and tools for later developments. Chapter two studies Decision-Making problems under certainty. The basic tool is the vector valué function, which represents imprecisión in the DM's preferences. We propose a characterization of the valué efficient set and different approximations with nesting and convergence properties. Several interactive algorithms complement the theoretical results. We devote Chapter three to problems under uncertainty. The development is parallel to the former and uses vector utility functions to model the DM's preferences. We introduce utility efficiency for simple distributions, its characterization and some approximations, which we partially extend to discrete and continuous classes of distributions. Chapter four studies the problem under fuzziness, at an exploratory level. We conclude with several open problems

Dominance intensity measure within fuzzy weight oriented MAUT: an application

We introduce a dominance intensity measuring method to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision-making problems on the basis of multi-attribute utility theory (MAUT) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers’ preferences, and imprecise weights are represented by trapezoidal fuzzy weights.The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights. An example concerning the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides illustrates the approach. Monte Carlo simulation techniques have been used to show that the proposed method performs well for different imprecision levels in terms of a hit ratio and a rank-order correlation measure

Dominance measuring methods within MAVT/MAUT with imprecise information concerning decision-makers'preferences

Dominance measuring methods are an approach for dealing with complex decision-making problems with imprecise information within multi-attribute value/utility theory. 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 review dominance measuring methods proposed in the literature for dealing with imprecise information (intervals, ordinal information or fuzzy numbers) about decision-makers? preferences and their performance in comparison with other existing approaches, like SMAA and SMAA-II or Sarabando and Dias? method

Ordenación de las alternativas basándose en intervalos de veto y ajuste

En este trabajo se presenta un método de ordenación de alternativas para problemas de toma de decisiones multicriterio en grupo, donde se conoce la importancia relativa de los decisores involucrados y sus preferencias se representan mediante una función de utilidad multiatributo aditiva. Suponemos que los decisores pueden definir un umbral de veto para los distintos criterios. El método propuesto identifica un intervalo de veto y otro de ajuste a partir de los vetos individuales proporcionados por cada decisor para cada uno de los criterios y, a partir de ellos, construye una función de veto, que permitirá vetar aquellas alternativas que tomen valores en la intervalo de veto; y una función de ajuste, que disminuirá la utilidad de las alternativas cuando contengan algún valor en un atributo dentro del intervalo de ajuste. Ambas funciones se incorporan convenientemente en el modelo en utilidad multiatributo aditivo para obtener una ordenación final de las alternativas consideradas

Veto values in Group Decision Making within MAUT: aggregating complete rankings derived from dominance intensity measures

We consider a groupdecision-making problem within multi-attribute utility theory, in which the relative importance of decisionmakers (DMs) is known and their preferences are represented by means of an additive function. We allow DMs to provide veto values for the attribute under consideration and build veto and adjust functions that are incorporated into the additive model. Veto functions check whether alternative performances are within the respective veto intervals, making the overall utility of the alternative equal to 0, where as adjust functions reduce the utilty of the alternative performance to match the preferences of other DMs. Dominance measuring methods are used to account for imprecise information in the decision-making scenario and to derive a ranking of alternatives for each DM. Specifically, ordinal information about the relative importance of criteria is provided by each DM. Finally, an extension of Kemeny's method is used to aggregate the alternative rankings from the DMs accounting for the irrelative importance

Dominance Measuring Approach using Stochastic Weights

In this paper we propose an approach to obtain a ranking of alternatives in multicriteria decision-making problems when there is imprecision concerning the alternative performances, component utility functions and weights. We assume decision maker's preferences are represented by an additive multi-attribute utility function, in which weights are modeled by independent normal variables, the performance in each attribute for each alternative is an interval value and classes of utility functions are available for each attribute. The approach we propose is based on dominance measures, which are computed in a similar way that when the imprecision concerning weights is modeled by uniform distributions or by an ordinal relation. In this paper we will show how the approach can be applied when the imprecision concerning weights are represented by normal distributions. Extensions to other distributions, such as truncated normal or beta, can be feasible using Monte Carlo simulation techniques

Ordenación de las alternativas basándose en la intesidad de dominancia y la lógica difusa

Se introduce un nuevo método de ordenación de las alternativas en un problema de decisión multicriterio con imprecisión en la información proporcionada por el decisor, representada por una función de utilidad multiatributo aditiva. Donde las consecuencias de las alternativas se representan mediante distribuciones uniformes, las funciones de utilidad de cada atributo son clases de funciones de utilidad y los pesos asociados a los atributos son números difusos triangulares (trapezoidales)

Ranking Alternatives on the Basis of a Dominance Intensity Measure

The additive multi-attribute utility model is widely used within MultiAttribute Utility Theory (MAUT), demanding all the information describing the decision-making situation. However, these information requirements can obviously be far too strict in many practical situations. Consequently, incomplete information about input parameters has been incorporated into the decisionmaking process. We propose an approach based on a dominance intensity measure to deal with such situations. The approach is based on the dominance values between pairs of alternatives that can be computed by linear programming. These dominance values are transformed into dominance intensities from which a dominance intensity measure is derived. It is used to analyze the robustness of a ranking of technologies for the disposition of surplus weapons-grade plutonium by the Department of Energy in the USA, and compared with other dominance measuring methods