Preference intensity in MCDM when an additive utility function represents DM preferences

We propose a new method for ranking 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 multiattribute utility function, in which weights can be modeled by independent normal variables, fuzzy numbers, value intervals or by an ordinal relation. The approaches are based on dominance measures or exploring the weight space in order to describe which ratings would make each alternative the preferred one. On the one hand, the approaches based on dominance measures compute the minimum utility difference among pairs of alternatives. Then, they compute a measure by which to rank the alternatives. On the other hand, the approaches based on exploring the weight space compute confidence factors describing the reliability of the analysis. These methods are compared using Monte Carlo simulation.

Dominance intensity methods for ranking of alternatives in mcdm with imprecise information

Los decisores cada vez se enfrentan a problemas más complejos en los que tomar una decisión implica tener que considerar simultáneamente muchos criterios que normalmente son conflictivos entre sí. En la mayoría de los problemas de decisión es necesario considerar criterios económicos, sociales y medioambientales. La Teoría de la Decisión proporciona el marco adecuado para poder ayudar a los decisores a resolver estos problemas de decisión complejos, al permitir considerar conjuntamente la incertidumbre existente sobre las consecuencias de cada alternativa en los diferentes atributos y la imprecisión sobre las preferencias de los decisores. En esta tesis doctoral nos centramos en la imprecisión de las preferencias de los decisores cuando éstas pueden ser representadas mediante una función de utilidad multiatributo aditiva. Por lo tanto, consideramos imprecisión tanto en los pesos como en las funciones de utilidad componentes de cada atributo. Se ha considerado el caso en que la imprecisión puede ser representada por intervalos de valores o bien mediante información ordinal, en lugar de proporcionar valores concretos. En este sentido, hemos propuesto métodos que permiten ordenar las diferentes alternativas basados en los conceptos de intensidad de dominación o intensidad de preferencia, los cuales intentan medir la fuerza con la que cada alternativa es preferida al resto. Para todos los métodos propuestos se ha analizado su comportamiento y se ha comparado con los más relevantes existentes en la literatura científica que pueden ser aplicados para resolver este tipo de problemas. Para ello, se ha realizado un estudio de simulación en el que se han usado dos medidas de eficiencia (hit ratio y coeficiente de correlación de Kendall) para comparar los diferentes métodos. ABSTRACT Decision makers increasingly face complex decision-making problems where they have to simultaneously consider many often conflicting criteria. In most decision-making problems it is necessary to consider economic, social and environmental criteria. Decision making theory provides an adequate framework for helping decision makers to make complex decisions where they can jointly consider the uncertainty about the performance of each alternative for each attribute, and the imprecision of the decision maker's preferences. In this PhD thesis we focus on the imprecision of the decision maker's preferences represented by an additive multiattribute utility function. Therefore, we consider the imprecision of weights, as well as of component utility functions for each attribute. We consider the case in which the imprecision is represented by ranges of values or by ordinal information rather than precise values. In this respect, we propose methods for ranking alternatives based on notions of dominance intensity, also known as preference intensity, which attempt to measure how much more preferred each alternative is to the others. The performance of the propose methods has been analyzed and compared against the leading existing methods that are applicable to this type of problem. For this purpose, we conducted a simulation study using two efficiency measures (hit ratio and Kendall correlation coefficient) to compare the different methods.

Designing Efficient Subsidy Policies in a Regional Economy: A Multicriteria Decision-Making (MCDM)-Computable General Equilibrium (CGE) Approach

Since policy-makers usually pursue several conflicting objectives, policy-making can be understood as a multicriteria decision problem. Following the methodological proposal by André and Cardenete (2005) André, F. J. and Cardenete, M. A. 2005. Multicriteria Policy Making. Defining Efficient Policies in a General Equilibrium Model, Seville: Centro de Estudios Andaluces. Working Paper No. E2005/04, multi-objective programming is used in connection with a computable general equilibrium model to represent optimal policy-making and to obtain so-called efficient policies in an application to a regional economy (Andalusia, Spain). This approach is applied to the design of subsidy policies under two different scenarios. In the first scenario, it is assumed that the government is concerned just about two objectives: ensuring the profitability of a key strategic sector and increasing overall output. Finally, the scope of the exercise is enlarged by solving a problem with seven policy objectives, including both general and sectorial objectives. It is concluded that the observed policy could have been Pareto-improved in several directions.

Municipal solid waste management system: decision support through systems analysis

Thesis submitted to the Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia for the degree of Doctor of Philosophy in Environmental Engineering

New directions in Stochastic Multicriteria Acceptability Analysis

Decisions taken in modern organizations are often multi-dimensional, involving multiple decision makers and several criteria measured on different scales. Multiple Criteria Decision Making (MCDM) methods are designed to analyze and to give recommendations in this kind of situations. Among the numerous MCDM methods, two large families of methods are the multi-attribute utility theory based methods and the outranking methods. Traditionally both method families require exact values for technical parameters and criteria measurements, as well as for preferences expressed as weights. Often it is hard, if not impossible, to obtain exact values. Stochastic Multicriteria Acceptability Analysis (SMAA) is a family of methods designed to help in this type of situations where exact values are not available. Different variants of SMAA allow handling all types of MCDM problems. They support defining the model through uncertain, imprecise, or completely missing values. The methods are based on simulation that is applied to obtain descriptive indices characterizing the problem. In this thesis we present new advances in the SMAA methodology. We present and analyze algorithms for the SMAA-2 method and its extension to handle ordinal preferences. We then present an application of SMAA-2 to an area where MCDM models have not been applied before: planning elevator groups for high-rise buildings. Following this, we introduce two new methods to the family: SMAA-TRI that extends ELECTRE TRI for sorting problems with uncertain parameter values, and SMAA-III that extends ELECTRE III in a similar way. An efficient software implementing these two methods has been developed in conjunction with this work, and is briefly presented in this thesis. The thesis is closed with a comprehensive survey of SMAA methodology including a definition of a unified framework.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Suitability of LiDAR technology for forest inventory in Russia

LiDAR is an advanced remote sensing technology with many applications, including forest inventory. The most common type is ALS (airborne laser scanning). The method is successfully utilized in many developed markets, where it is replacing traditional forest inventory methods. However, it is innovative for Russian market, where traditional field inventory dominates. ArboLiDAR is a forest inventory solution that engages LiDAR, color infrared imagery, GPS ground control plots and field sample plots, developed by Arbonaut Ltd. This study is an industrial market research for LiDAR technology in Russia focused on customer needs. Russian forestry market is very attractive, because of large growing stock volumes. It underwent drastic changes in 2006, but it is still in transitional stage. There are several types of forest inventory, both with public and private funding. Private forestry enterprises basically need forest inventory in two cases – while making coupe demarcation before timber harvesting and as a part of forest management planning, that is supposed to be done every ten years on the whole leased territory. The study covered 14 companies in total that include private forestry companies with timber harvesting activities, private forest inventory providers, state subordinate companies and forestry software developer. The research strategy is multiple case studies with semi-structured interviews as the main data collection technique. The study focuses on North-West Russia, as it is the most developed Russian region in forestry. The research applies the Voice of the Customer (VOC) concept to elicit customer needs of Russian forestry actors and discovers how these needs are met. It studies forest inventory methods currently applied in Russia and proposes the model of method comparison, based on Multi-criteria decision making (MCDM) approach, mainly on Analytical Hierarchy Process (AHP). Required product attributes are classified in accordance with Kano model. The answer about suitability of LiDAR technology is ambiguous, since many details should be taken into account.

Teoria dei giochi e Multi-criteria decision-making per reti mobili Ad-hoc: un protocollo di routing

Nell'elaborato si analizzano aspetti della teoria dei giochi e della multi-criteria decision-making. La riflessione serve a proporre le basi per un nuovo modello di protocollo di routing in ambito Mobile Ad-hoc Networks. Questo prototipo mira a generare una rete che riesca a gestirsi in maniera ottimale grazie ad un'acuta tecnica di clusterizzazione. Allo stesso tempo si propone come obiettivo il risparmio energetico e la partecipazione collaborativa di tutti i componenti.

Applying the fuzzy analytical hierarchy process in digital marketing

The fuzzy analytical network process (FANP) is introduced as a potential multi-criteria-decision-making (MCDM) method to improve digital marketing management endeavors. Today’s information overload makes digital marketing optimization, which is needed to continuously improve one’s business, increasingly difficult. The proposed FANP framework is a method for enhancing the interaction between customers and marketers (i.e., involved stakeholders) and thus for reducing the challenges of big data. The presented implementation takes realities’ fuzziness into account to manage the constant interaction and continuous development of communication between marketers and customers on the Web. Using this FANP framework, the marketers are able to increasingly meet the varying requirements of their customers. To improve the understanding of the implementation, advanced visualization methods (e.g., wireframes) are used.

Continuous multi-criteria methods for crop and soil conservation planning on La Colacha (Río Cuarto, Province of Cordoba, Argentina)

Agro-areas of Arroyos Menores (La Colacha) west and south of Rand south of R?o Cuarto (Prov. of Cordoba, Argentina) basins are very fertile but have high soil loses. Extreme rain events, inundations and other severe erosions forming gullies demand urgently actions in this area to avoid soil degradation and erosion supporting good levels of agro production. The authors first improved hydrologic data on La Colacha, evaluated the systems of soil uses and actions that could be recommended considering the relevant aspects of the study area and applied decision support systems (DSS) with mathematic tools for planning of defences and uses of soils in these areas. These were conducted here using multi-criteria models, in multi-criteria decision making (MCDM); first of discrete MCDM to chose among global types of use of soils, and then of continuous MCDM to evaluate and optimize combined actions, including repartition of soil use and the necessary levels of works for soil conservation and for hydraulic management to conserve against erosion these basins. Relatively global solutions for La Colacha area have been defined and were optimised by Linear Programming in Goal Programming forms that are presented as Weighted or Lexicographic Goal Programming and as Compromise Programming. The decision methods used are described, indicating algorithms used, and examples for some representative scenarios on La Colacha area are given.

A Recommendation Framework Based on the Analytic Network Process and its Application in the Semantic Technology Domain

When users face a certain problem needing a product, service, or action to solve it, selecting the best alternative among them can be a dicult task due to the uncertainty of their quality. This is especially the case in the domains where users do not have an expertise, like for example in Software Engineering. Multiple criteria decision making (MCDM) methods are methods that help making better decisions when facing the complex problem of selecting the best solution among a group of alternatives that can be compared according to different conflicting criteria. In MCDM problems, alternatives represent concrete products, services or actions that will help in achieving a goal, while criteria represent the characteristics of these alternatives that are important for making a decision.

Systematic Approach for the selection of monitoring technologies in CO2 geological storage projects. Application of multicriteria decision making

Geologic storage of carbon dioxide (CO2) has been proposed as a viable means for reducing anthropogenic CO2 emissions. Once injection begins, a program for measurement, monitoring, and verification (MMV) of CO2 distribution is required in order to: a) research key features, effects and processes needed for risk assessment; b) manage the injection process; c) delineate and identify leakage risk and surface escape; d) provide early warnings of failure near the reservoir; and f) verify storage for accounting and crediting. The selection of the methodology of monitoring (characterization of site and control and verification in the post-injection phase) is influenced by economic and technological variables. Multiple Criteria Decision Making (MCDM) refers to a methodology developed for making decisions in the presence of multiple criteria. MCDM as a discipline has only a relatively short history of 40 years, and it has been closely related to advancements on computer technology. Evaluation methods and multicriteria decisions include the selection of a set of feasible alternatives, the simultaneous optimization of several objective functions, and a decision-making process and evaluation procedures that must be rational and consistent. The application of a mathematical model of decision-making will help to find the best solution, establishing the mechanisms to facilitate the management of information generated by number of disciplines of knowledge. Those problems in which decision alternatives are finite are called Discrete Multicriteria Decision problems. Such problems are most common in reality and this case scenario will be applied in solving the problem of site selection for storing CO2. Discrete MCDM is used to assess and decide on issues that by nature or design support a finite number of alternative solutions. Recently, Multicriteria Decision Analysis has been applied to hierarchy policy incentives for CCS, to assess the role of CCS, and to select potential areas which could be suitable to store. For those reasons, MCDM have been considered in the monitoring phase of CO2 storage, in order to select suitable technologies which could be techno-economical viable. In this paper, we identify techniques of gas measurements in subsurface which are currently applying in the phase of characterization (pre-injection); MCDM will help decision-makers to hierarchy the most suitable technique which fit the purpose to monitor the specific physic-chemical parameter.

Selección de una cartera de acciones bajo criterios de sostenibilidad medioambiental empleando técnicas de decisión multicriterio

La apertura de los mercados internacionales de capital como consecuencia del proceso de globalización ha motivado un aumento significativo de la labor investigadora en el campo de la economía y, concretamente, en la teoría de la inversión. Los trabajos en este área tuvieron como punto de partida el artículo publicado por Harry Markowitz en 1952 en el Journal of Finance bajo el título “Portfolio Selection”. En él se pretende hacer una modelización del proceso inversionista principalmente a través de dos criterios: riesgo y retorno. Markowitz no da indicaciones en cuanto a cómo elegir la composición de una cartera optimizando simultáneamente riesgo y retorno. En su lugar, fija una de las dos variables (según la aversión al riesgo del inversor y su preferencia por las ganancias) y optimiza la otra. Sin embargo, este análisis resulta ser bastante simplista si tenemos en cuenta que los inversores, como cualquier ser humano, son decisores multicriterio: no sólo maximizarán el beneficio para un riesgo dado, sino que intentarán también minimizar el riesgo, diversificar el tipo de acciones que poseen para inmunizarse frente a crisis financieras, emplear nuevos criterios de inversión que incorporen la sostenibilidad medioambiental y el impacto que la actividad productiva tiene en la sociedad, destinar un mayor porcentaje del presupuesto a compañías poco endeudadas, que alcancen un buen rating o unos buenos índices de responsabilidad social corporativa, etc. La inclusión de estas nuevas variables en el modelo tradicional es ahora posible gracias a la teoría de la decisión multicriterio (MCDM: Multiple Criteria Decision Making). Desde los años setenta se viene desarrollando y aplicando este nuevo paradigma en áreas tan dispares como la planificación de redes de telecomunicación, la optimización de listas de espera en hospitales o la planificación logística de las grandes distribuidoras y compañías de mensajería. En el presente trabajo se pretende aplicar el paradigma MCDM a la construcción de una cartera de acciones siguiendo criterios tanto puramente financieros como de sostenibilidad medioambiental y responsabilidad social corporativa. Para ello, en esta primera parte se estudiará la teoría clásica de selección de carteras de Markowitz, explicando los parámetros que permiten caracterizar un instrumento financiero individual (retorno, riesgo, covarianza) y una cartera de instrumentos (diversificación, frontera eficiente). En la segunda parte se analizará en profundidad el concepto de desarrollo sostenible, tan extendido en la actualidad, y su transposición al plano corporativo y de gestión de carteras. Se realizará una revisión histórica del término y su encaje en el esquema de decisión de una compañía privada, así como un estudio de las herramientas para medir el cumplimiento de ciertos principios de sostenibilidad por parte de las compañías y hacer, de esta forma, cuantificables dichos conceptos con vistas a su incorporación al esquema decisional del inversor. Con posterioridad, en la tercera parte se estudiará la programación por metas como técnica de decisión multicriterio para aplicar al problema de la composición de carteras. El potencial de esta metodología radica en que permite hacer resoluble un problema, en principio, sin solución. Y es que, como no se pueden optimizar todos y cada uno de los criterios simultáneamente, la programación por metas minimizará las desviaciones respecto a determinados niveles de aspiración para ofrecer una solución lo más cercana posible a la ideal. Finalmente, se construirá un caso de estudio a partir de datos reales tanto financieros como de sostenibilidad para, posteriormente, resolver el modelo matemático construido empleando LINGO. A través de esta herramienta software se podrá simular el proceso de optimización y obtener una cartera-solución que refleje las preferencias del agente decisor.

Discrete Multi-Criteria Methods for lands use and conservation planning on La Colacha in Arroyos Menores (Río Cuarto, Province of Córdoba, Argentina)

The study area is La Colacha sub-basins from Arroyos Menores basins, natural areas at West and South of Río Cuarto in Province of Córdoba of Argentina, fertile with loess soils and monsoon temperate climate, but with soil erosions including regressive gullies that degrade them progressively. Cultivated gently since some hundred sixty years, coordinated action planning became necessary to conserve lands while keeping good agro-production. The authors had improved data on soils and on hydrology for the study area, evaluated systems of soil uses and actions to be recommended and applied Decision Support Systems (DSS) tools for that, and were conducted to use discrete multi-criteria models (MCDM) for the more global views about soil conservation and hydraulic management actions and about main types of use of soils. For that they used weighted PROMETHEE, ELECTRE, and AHP methods with a system of criteria grouped as environmental, economic and social, and criteria from their data on effects of criteria. The alternatives resulting offer indication for planning depending somehow on sub basins and on selections of weights, but actions for conservation of soils and water management measures are recommended to conserve the basins conditions, actually sensibly degrading, mainly keeping actual uses of the lands.

Desarrollo de un algoritmo de decisión multicriterio para la gestión de listas de espera en la solicitud de Holter

Las listas de espera son un problema para la mayor parte de los países que cuentan con un Sistema Nacional de Salud. El presente trabajo propone analizar el problema de las listas de espera desde una perspectiva de Decisión Multicriterio. Tras un análisis de las diferentes metodologías existentes, hemos elaborado un modelo de decisión basado en el método AHP (Analytic Hierarchy Process) para la gestión de listas de espera y lo hemos aplicado a un Hospital de la Comunidad de Madrid. La decisión multicriterio MCDM (Multiple Criteria Decision Making) es la teoría que estudia y analiza los problemas de decisión que involucran diferentes criterios. La MCDM enmarca con precisión problemas reales de toma de decisiones, planteados usualmente haciendo uso de varios criterios en conflicto; en los cuales, no será posible obtener en general una solución que asigne a todos los criterios su mejor valor sino que el decisor, aplicando distintas técnicas, deberá decidir la mejor solución a escoger del conjunto de soluciones factibles. El fundamento del AHP radica en descomponer problemas complejos en otros más sencillos y agregar las soluciones de los mismos. Según la propuesta de Saaty, el primer paso para la aplicación de este método es estructurar jerárquicamente el problema en niveles con distintos nodos interconectados. El primer nivel de la jerarquía corresponde al propósito del problema, el nivel/niveles intermedios a los criterios/subcriterios en base a los cuales se forma la decisión y el último corresponde a las alternativas o soluciones factibles del problema. La aplicación del método AHP requiere: -Realizar comparaciones por pares entre los entes de cada nivel jerárquico, en base a la importancia que presentan para el nodo del nivel superior de la jerarquía al que están ligados. Los resultados de estas comparaciones se recogen en forma de matrices de comparación por pares. -Obtener los vectores de prioridad correspondientes a cada una de las matrices de comparación por pares. -Calcular la contribución de cada alternativa al propósito del problema, mediante una agregación multiplicativa entre los niveles jerárquicos y en función de estos valores, ordenar las alternativas y seleccionar lo más conveniente como solución del problema. Como último paso en la metodología AHP debemos señalar que, cualquiera que sea el método empleado para sintetizar la información de dichas matrices para determinar los vectores de prioridad de los entes que se comparan, es posible realizar un análisis de sensibilidad del resultado alcanzado, visualizando y analizando otras posibles soluciones a obtener haciendo cambios en los juicios de valor emitidos por la unidad decisora al construir dichas matrices. El software Expert-Choice permite realizar el análisis de sensibilidad de 5 formas diferentes. En estos análisis se realizan variaciones en el valor de un peso o prioridad y se observa numérica y gráficamente como este cambio afecta a la puntuación de las alternativas.