17 research outputs found

    Decision Support under Risk by Optimization of Scenario Importance Weighted OWA Aggregations, Journal of Telecommunications and Information Technology, 2009, nr 3

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    The problem of evaluation outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. TheWOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e., to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective functions related to decisions under risk. Linear programming formulations are introduced for optimization of the WOWA objective representing risk averse preferences. Their computational efficiency is demonstrated

    Indicators for the characterization of discrete Choquet integrals

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    Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context

    Quantitative risk assessment, aggregation functions and capital allocation problems

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    [eng] This work is focused on the study of risk measures and solutions to capital allocation problems, their suitability to answer practical questions in the framework of insurance and 铿乶ancial institutions and their connection with a family of functions named aggregation operators. These operators are well-known among researchers from the information sciences or fuzzy sets and systems community. The 铿乺st contribution of this dissertation is the introduction of GlueVaR risk measures, a family belonging to the more general class of distortion risk measures. GlueVaR risk measures are simple to understand for risk managers in the 铿乶ancial and insurance sectors, because they are based on the most popular risk measures (VaR and TVaR) in both industries. For the same reason, they are almost as easy to compute as those common risk measures and, moreover, GlueVaR risk measures allow to capture more intricated managerial and regulatory attitudes towards risk. The de铿乶ition of the tail-subadditivity property for a pair of risks may be considered the second contribution. A distortion risk measure which satis铿乪s this property has the ability to be subadditive in extremely adverse scenarios. In order to decide if a GlueVaR risk measure is a candidate to satisfy the tail-subadditivity property, conditions on its parameters are determined. It is shown that distortion risk measures and several ordered weighted averaging operators in the discrete 铿乶ite case are mathematically linked by means of the Choquet integral. It is shown that the overall aggregation preference of the expert may be measured by means of the local degree of orness of the distortion risk measure, which is a concept taken over from the information sciences community and brung into the quantitative risk management one. New indicators for helping to characterize the discrete Choquet integral are also presented in this dissertation. The aim is complementing those already available, in order to be able to highlight particular features of this kind of aggregation function. Following this spirit, the degree of balance, the divergence, the variance indicator and R茅nyi entropies as indicators within the framework of the Choquet integral are here introduced. A major contribution derived from the relationship between distortion risk measures and aggregation operators is the characterization of the risk attitude implicit into the choice of a distortion risk measure and a con铿乨ence or tolerance level. It is pointed out that the risk attitude implicit in a distortion risk measure is to some extent contained in its distortion function. In order to describe some relevant features of the distortion function, the degree of orness indicator and a quotient function are used. It is shown that these mathematical devices give insights on the implicit risk behavior involved in risk measures and entail the de铿乶itions of overall, absolute and speci铿乧 risk attitudes. Regarding capital allocation problems, a list of key elements to delimit these problems is provided and mainly two contributions are made. Firstly, it is shown that GlueVaR risk measures are as useful as other alternatives like VaR or TVaR to solve capital allocation problems. The second contribution is understanding capital allocation principles as compositional data. This interpretation of capital allocation principles allows the connection between aggregation operators and capital allocation problems, with an immediate practical application: Properly averaging several available solutions to the same capital allocation problem. This thesis contains some preliminary ideas on this connection, but it seems to be a promising research 铿乪ld.[spa] Este trabajo se centra en el estudio de medidas de riesgo y de soluciones a problemas de asignaci贸n de capital, en su capacidad para responder cuestiones pr谩cticas en el 谩mbito de las instituciones aseguradoras y financieras, y en su conexi贸n con una familia de funciones denominadas operadores de agregaci贸n. Estos operadores son bien conocidos entre los investigadores de las comunidades de las ciencias de la informaci贸n o de los conjuntos y sistemas fuzzy. La primera contribuci贸n de esta tesis es la introducci贸n de las medidas de riesgo GlueVaR, una familia que pertenece a la clase m谩s general de las medidas de riesgo de distorsi贸n. Las medidas de riesgo GlueVaR son sencillas de entender para los gestores de riesgo de los sectores financiero y asegurador, puesto que est谩n basadas en las medidas de riesgo m谩s populares (el VaR y el TVaR) de ambas industrias. Por el mismo motivo, son casi tan f谩ciles de calcular como estas medidas de riesgo m谩s comunes pero, adem谩s, las medidas de riesgo GlueVaR permiten capturar actitudes de gesti贸n y regulatorias ante el riesgo m谩s complicadas. La definici贸n de la propiedad de la subadditividad en colas para un par de riesgos se puede considerar la segunda contribuci贸n. Una medida de riesgo de distorsi贸n que cumple esta propiedad tiene la capacidad de ser subadditiva en escenarios extremadamente adversos. Con el prop贸sito de decidir si una medida de riesgo GlueVaR es candidata a satisfacer la propiedad de la subadditividad en colas se determinan condiciones sobre sus par谩metros. Se muestra que las medidas de riesgo de distorsi贸n y varios operadores de medias ponderadas ordenadas en el caso finito y discreto est谩n matem谩ticamente relacionadas a trav茅s de la integral de Choquet. Se muestra que la preferencia global de agregaci贸n del experto puede medirse usando el nivel local de orness de la medida de riesgo de distorsi贸n, que es un concepto trasladado des de la comunidad de las ciencias de la informaci贸n hacia la comunidad de la gesti贸n cuantitativa del riesgo. Nuevos indicadores para ayudar a caracterizar las integrales de Choquet en el caso discreto tambi茅n se presentan en esta disertaci贸n. Se pretende complementar a los existentes, con el fin de ser capaces de destacar caracter铆sticas particulares de este tipo de funciones de agregaci贸n. Con este esp铆ritu, se presentan el nivel de balance, la divergencia, el indicador de varianza y las entrop铆as de R茅nyi como indicadores en el 谩mbito de la integral de Choquet. Una contribuci贸n relevante que se deriva de la relaci贸n entre las medidas de riesgo de distorsi贸n y los operadores de agregaci贸n es la caracterizaci贸n de la actitud ante el riesgo impl铆cita en la elecci贸n de una medida de riesgo de distorsi贸n y de un nivel de confianza. Se se帽ala que la actitud ante el riesgo impl铆cita en una medida de riesgo de distorsi贸n est谩 contenida, hasta cierto punto, en su funci贸n de distorsi贸n. Para describir algunos rasgos relevantes de la funci贸n de distorsi贸n se usan el indicador nivel de orness y una funci贸n cociente. Se muestra que estos instrumentos matem谩ticos aportan informaci贸n relativa al comportamiento ante el riesgo impl铆cito en las medidas de riesgo, y que de ellos se derivan las definiciones de les actitudes ante el riego de tipo general, absoluto y espec铆fico. En cuanto a los problemas de asignaci贸n de capital, se proporciona un listado de elementos clave para delimitar estos problemas y se hacen principalmente dos contribuciones. En primer lugar, se muestra que las medidas de riesgo GlueVaR son tan 煤tiles como otras alternativas tales como el VaR o el TVaR para resolver problemas de asignaci贸n de capital. La segunda contribuci贸n consiste en entender los principios de asignaci贸n de capital como datos composicionales. Esta interpretaci贸n de los principios de asignaci贸n de capital permite establecer conexi贸n entre los operadores de agregaci贸n y los problemas de asignaci贸n de capital, con una aplicaci贸n pr谩ctica inmediata: calcular debidamente la media de diferentes soluciones disponibles para el mismo problema de asignaci贸n de capital. Esta tesis contiene algunas ideas preliminares sobre esta conexi贸n, pero parece un campo de investigaci贸n prometedor

    Journal of Telecommunications and Information Technology, 2008, nr 4

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    kwartalni

    Journal of Telecommunications and Information Technology, 2009, nr 3

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    kwartalni

    Multiple Criteria Analysis of Discrete Alternatives with a Simple Preference Specification: Pairwise-outperformance based Approaches

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    Many methods have been developed for multiple criteria analysis and/or ranking of discrete alternatives. Most of them require complex specification of preferences. Therefore, they are not applicable for problems with numerous alternatives and/or criteria, where preference specification by the decision makers can hardly be done in a way acceptable for small problems, e.g., for pair-wise comparisons. In this paper we describe several new methods implemented for a real-life application dealing with muti-criteria analysis of future energy technologies. This analysis involves large numbers of both altrnatives and criteria. Moreover, the analysis was made by a large number of stakeholders without expeience in analytical methods. Therefore, a simple method for interactive preference specification was a condition for the analysis. The paper presents a number of new methods based on the developed out performance aggregations that take into account inter-alternative factors. Finally, a comparison of methods and experience of using them is discussed

    Study of Advanced Propulsion Systems for Small Transport Aircraft Technology (STAT) Program

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    Definitions of takeoff gross weight, performance, and direct operating cost for both a 30 and 50 passenger airplane were established. The results indicate that a potential direct operating cost benefit, resulting from advanced technologies, of approximately 20 percent would be achieved for the 1990 engines. Of the numerous design features that were evaluated, only maintenance-related items contributed to a significant decrease in direct operating cost. Recommendations are made to continue research and technology programs for advanced component and engine development
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