The non-existence of a utility function and the structure of non-representable preference relations

In this paper we investigate the structure of non-representable preference relations. While there is a vast literature on different kinds of preference relations that can be represented by a real-valued utility function, very little is known or understood about preference relations that cannot be represented by a real-valued utility function. There has been no systematic analysis of the non-representation problem. In this paper we give a complete description of non-representable preference relations which are total preorders or chains. We introduce and study the properties of four classes of non-representable chains: long chains, planar chains, Aronszajn-like chains and Souslin chains. In the main theorem of the paper we prove that a chain is non-representable if and only it is a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. (C) 2002 Published by Elsevier Science B.V.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bell-man-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (< X, M > models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called < X, R > models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example. (c) 2007 Elsevier Inc. All rights reserved.

Fuzzy tolerance/equivalence relations from intersection, union and complement operators and their application to a clustering method

This master thesis work introduces the fuzzy tolerance/equivalence relation and its application in cluster analysis. The work presents about the construction of fuzzy equivalence relations using increasing generators. Here, we investigate and research on the role of increasing generators for the creation of intersection, union and complement operators. The objective is to develop different varieties of fuzzy tolerance/equivalence relations using different varieties of increasing generators. At last, we perform a comparative study with these developed varieties of fuzzy tolerance/equivalence relations in their application to a clustering method.

A flexible consensus scheme for multicriteria group decision making under linguistic assessments

The present paper proposes a flexible consensus scheme for group decision making, which allows one to obtain a consistent collective opinion, from information provided by each expert in terms of multigranular fuzzy estimates. It is based on a linguistic hierarchical model with multigranular sets of linguistic terms, and the choice of the most suitable set is a prerogative of each expert. From the human viewpoint, using such model is advantageous, since it permits each expert to utilize linguistic terms that reflect more adequately the level of uncertainty intrinsic to his evaluation. From the operational viewpoint, the advantage of using such model lies in the fact that it allows one to express the linguistic information in a unique domain, without losses of information, during the discussion process. The proposed consensus scheme supposes that the moderator can interfere in the discussion process in different ways. The intervention can be a request to any expert to update his opinion or can be the adjustment of the weight of each expert`s opinion. An optimal adjustment can be achieved through the execution of an optimization procedure that searches for the weights that maximize a corresponding soft consensus index. In order to demonstrate the usefulness of the presented consensus scheme, a technique for multicriteria analysis, based on fuzzy preference relation modeling, is utilized for solving a hypothetical enterprise strategy planning problem, generated with the use of the Balanced Scorecard methodology. (C) 2009 Elsevier Inc. All rights reserved.

Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease) and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA) and by fuzzy max-min compositions (fuzzy), and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

Quasi-Transitive and Suzumura Consistent Relations

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, together with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is strictly weaker than transitivity but in the case of collective choice rules that satisfy further properties, the conjunction of quasi- transitivity and Suzumura consistency implies transitivity of the social relation. We prove this observation by characterizing the Pareto rule as the only collective choice rule such that collective preference relations are quasi-transitive and Suzumura consistent but not necessarily complete.

Reward-risk efficiency in proportional reinsurance with different risk measures

We have studied, in particular under normality of the implied random variables, the connections between different measures of risk such as the standard deviation, the W-ruin probability and the p-V@R. We discuss conditions granting the equivalence of these measures with respect to risk preference relations and the equivalence of dominance and efficiency of risk-reward criteria involving these measures. Then more specifically we applied these concepts to rigorously face the problem of finding the efficient set of de Finetti’s variable quota share proportional reinsurance.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Predestination and the Protestant ethic

This paper shows an equivalence result between the utility functions of secularagents who abide by a moral obligation to accumulate wealth and those of religiousagents who believe that salvation is immutable and preordained by God. Thisresult formalizes Weber's renowned thesis on the connection between the worldlyasceticism of Protestants and the religious premises of Calvinism. Furthermore,ongoing economies are often modeled with preference relations such as "Keeping upwith the Joneses" which are not associated with religion. Our results relate thesesecular economies of today and economies of the past shaped by religious ideas.

A theory of reference-dependent behavior

Extensive field and experimental evidence in a variety of environments show that behavior depends on a reference point. This paper provides an axiomatic characterization of this dependence. We proceed by imposing gradually more structure on both choice correspondences and preference relations, requiring increasingly higher levels of rationality, and freeing the decision-maker from certain types of inconsistencies. The appropriate degree of behavioral structure will depend on the phenomenon that is to be modeled. Lastly, we provide two applications of our work: one to model the status-quo bias, and another to model addictive behavior.

Learning Preferences with Kernel-Based Methods

Learning of preference relations has recently received significant attention in machine learning community. It is closely related to the classification and regression analysis and can be reduced to these tasks. However, preference learning involves prediction of ordering of the data points rather than prediction of a single numerical value as in case of regression or a class label as in case of classification. Therefore, studying preference relations within a separate framework facilitates not only better theoretical understanding of the problem, but also motivates development of the efficient algorithms for the task. Preference learning has many applications in domains such as information retrieval, bioinformatics, natural language processing, etc. For example, algorithms that learn to rank are frequently used in search engines for ordering documents retrieved by the query. Preference learning methods have been also applied to collaborative filtering problems for predicting individual customer choices from the vast amount of user generated feedback. In this thesis we propose several algorithms for learning preference relations. These algorithms stem from well founded and robust class of regularized least-squares methods and have many attractive computational properties. In order to improve the performance of our methods, we introduce several non-linear kernel functions. Thus, contribution of this thesis is twofold: kernel functions for structured data that are used to take advantage of various non-vectorial data representations and the preference learning algorithms that are suitable for different tasks, namely efficient learning of preference relations, learning with large amount of training data, and semi-supervised preference learning. Proposed kernel-based algorithms and kernels are applied to the parse ranking task in natural language processing, document ranking in information retrieval, and remote homology detection in bioinformatics domain. Training of kernel-based ranking algorithms can be infeasible when the size of the training set is large. This problem is addressed by proposing a preference learning algorithm whose computation complexity scales linearly with the number of training data points. We also introduce sparse approximation of the algorithm that can be efficiently trained with large amount of data. For situations when small amount of labeled data but a large amount of unlabeled data is available, we propose a co-regularized preference learning algorithm. To conclude, the methods presented in this thesis address not only the problem of the efficient training of the algorithms but also fast regularization parameter selection, multiple output prediction, and cross-validation. Furthermore, proposed algorithms lead to notably better performance in many preference learning tasks considered.

A Characterization of Consistent Collective Choice Rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference. The properties used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.

Predação em capítulos de picão-preto e sua relação com o tamanho e o grau de agrupamento das plantas

Com o objetivo de verificar possíveis correlações entre níveis de predação de capítulos de B. pilosa e o tamanho das plantas, bem como com o seu grau de agrupamento, o presente trabalho foi desenvolvido em áreas ruderais nos arredores da cidade de Botucatu, SP. em cada coleta, foram obtidos 15 indivíduos em fase reprodutiva, sendo dez deles provenientes de agrupamentos e cinco isolados, no período de março a setembro de 1993, totalizando seis coletas. Cada planta foi caracterizada quanto a parâmetros biométricos por meio de mensurações, contagens e determinação da biomassa das diferentes estruturas, avaliando-se também a ocorrência de predação nos capítulos. Nas duas condições de agrupamento, o tamanho das plantas foi altamente variável havendo, porém, maior freqüência nas menores classes de tamanho. de modo geral, não houve diferença significativa entre plantas agrupadas e isoladas no que se refere aos parâmetros biométricos analisados. Plantas maiores produziram maior número de capítulos e o nível de predação correlacionou-se positivamente com o tamanho das plantas, independentemente do grau de agrupamento das populações. A distribuição agrupada não condicionou, portanto, maiores níveis de predação, uma vez que plantas maiores dos dois grupos foram preferencialmente atacadas. Isto corrobora a Hipótese do Vigor proposta para explicar relações de preferência entre plantas e seus herbívoros.

Nuevo paradigma para decisiones colectivas en entornos no competitivos

La tesis estudia uno de los aspectos más importantes de la gestión de la sociedad de la información: conocer la manera en que una persona valora cualquier situación. Esto es importante para el individuo que realiza la valoración y para el entorno con el que se relaciona. La valoración es el resultado de la comparación: se asignan los mismos valores a alternativas similares y mayores valores a alternativas mejor consideradas en el proceso de comparación. Los patrones que guían al individuo a la hora de hacer la comparación se derivan de sus preferencias individuales (es decir, de sus opiniones). En la tesis se presentan varios procedimientos para establecer las relaciones de preferencia entre alternativas de una persona. La valoración progresa hasta obtener una representación numérica de sus preferencias. Cuando la representación de preferencias es homogénea permite, además, contrastar las preferencias personales con las del resto de evaluadores, lo que favorece la evaluación de políticas, la transferencia de información entre diferentes individuos y el diseño de la alternativa que mejor se adapte a las preferencias identificadas. Al mismo tiempo, con esta información se pueden construir comunidades de personas con los mismos sistemas de preferencias ante una cuestión concreta. La tesis muestra un caso de aplicación de esta metodología: optimización de las políticas laborales en un mercado real. Para apoyar a los demandantes de empleo (en su iniciación o reincorporación al mundo laboral o en el cambio de su actividad) es necesario conocer sus preferencias respecto a las ocupaciones que están dispuestos a desempeñar. Además, para que la intermediación laboral sea efectiva, las ocupaciones buscadas deben de ser ofrecidas por el mercado de trabajo y el demandante debe reunir las condiciones para acceder a esas ocupaciones. El siguiente desarrollo de estos modelos nos lleva a los procedimientos utilizados para transformar múltiples preferencias en una decisión agregada y que consideran tanto la opinión de cada uno de los individuos que participan en la decisión como las interacciones sociales, todo ello dirigido a generar una solución que se ajuste lo mejor posible al punto de vista de toda la población. Las decisiones con múltiples participantes inciden, principalmente, en: el aumento del alcance para incorporar a personas que tradicionalmente no han sido consideradas en las tomas de decisiones, la agregación de las preferencias de los múltiples participantes en las tomas de decisiones colectivas (mediante votación, utilizando aplicaciones desarrolladas para la Web2.0 y a través de comparaciones interpersonales de utilidad) y, finalmente, la auto-organización para permitir que interaccionen entre si los participantes en la valoración, de forma que hagan que el resultado final sea mejor que la mera agregación de opiniones individuales. La tesis analiza los sistemas de e-democracia o herramientas para su implantación que tienen más más utilización en la actualidad o son más avanzados. Están muy relacionados con la web 2.0 y su implantación está suponiendo una evolución de la democracia actual. También se estudian aplicaciones de software de Colaboración en la toma de decisiones (Collaborative decision-making (CDM)) que ayudan a dar sentido y significado a los datos. Pretenden coordinar las funciones y características necesarias para llegar a decisiones colectivas oportunas, lo que permite a todos los interesados participar en el proceso. La tesis finaliza con la presentación de un nuevo modelo o paradigma en la toma de decisiones con múltiples participantes. El desarrollo se apoya en el cálculo de las funciones de utilidad empática. Busca la colaboración entre los individuos para que la toma de decisiones sea más efectiva, además pretende aumentar el número de personas implicadas. Estudia las interacciones y la retroalimentación entre ciudadanos, ya que la influencia de unos ciudadanos en los otros es fundamental para los procesos de toma de decisiones colectivas y de e-democracia. También incluye métodos para detectar cuando se ha estancado el proceso y se debe interrumpir. Este modelo se aplica a la consulta de los ciudadanos de un municipio sobre la oportunidad de implantar carriles-bici y las características que deben tomar. Se simula la votación e interacción entre los votantes. ABSTRACT The thesis examines one of the most important aspects of the management of the information society: get to know how a person values every situation. This is important for the individual performing the assessment and for the environment with which he interacts. The assessment is a result of the comparison: identical values are allocated to similar alternatives and higher values are assigned to those alternatives that are more favorably considered in the comparison process. Patterns that guide the individual in making the comparison are derived from his individual preferences (ie, his opinions). In the thesis several procedures to establish preference relations between alternatives a person are presented. The assessment progresses to obtain a numerical representation of his preferences. When the representation of preferences is homogeneous, it also allows the personal preferences of each individual to be compared with those of other evaluators, favoring policy evaluation, the transfer of information between different individuals and design the alternative that best suits the identified preferences. At the same time, with this information you can build communities of people with similar systems of preferences referred to a particular issue. The thesis shows a case of application of this methodology: optimization of labour policies in a real market. To be able support jobseekers (in their initiation or reinstatement to employment or when changing area of professional activity) is necessary to know their preferences for jobs that he is willing to perform. In addition, for labour mediation to be effective occupations that are sought must be offered by the labour market and the applicant must meet the conditions for access to these occupations. Further development of these models leads us to the procedures used to transform multiple preferences in an aggregate decision and consider both the views of each of the individuals involved in the decision and the social interactions, all aimed at generating a solution that best fits of the point of view of the entire population. Decisions with multiple participants mainly focus on: increasing the scope to include people who traditionally have not been considered in decision making, aggregation of the preferences of multiple participants in collective decision making (by vote, using applications developed for the Web 2.0 and through interpersonal comparisons of utility) and, finally, self-organization to allow participants to interact with each other in the assessment, so that the final result is better than the mere aggregation of individual opinions. The thesis analyzes the systems of e-democracy or tools for implementation which are more popular or more advanced. They are closely related to the Web 2.0 and its implementation is bringing an evolution of the current way of understanding democracy. We have also studied Collaborative Decision-Making (CDM)) software applications in decision-making which help to give sense and meaning to the data. They intend to coordinate the functions and features needed to reach adequate collective decisions, allowing all stakeholders to participate in the process. The thesis concludes with the presentation of a new model or paradigm in decision-making with multiple participants. The development is based on the calculation of the empathic utility functions. It seeks collaboration between individuals to make decision-making more effective; it also aims to increase the number of people involved. It studies the interactions and feedback among citizens, because the influence of some citizens in the other is fundamental to the process of collective decision-making and e-democracy. It also includes methods for detecting when the process has stalled and should be discontinued. This model is applied to the consultation of the citizens of a municipality on the opportunity to introduce bike lanes and characteristics they should have. Voting and interaction among voters is simulated.