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

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

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

[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 financial 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 first 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 financial 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 definition of the tail-subadditivity property for a pair of risks may be considered the second contribution. A distortion risk measure which satisfies 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 finite 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 Rényi 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 confidence 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 definitions of overall, absolute and specific 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 field.[spa] Este trabajo se centra en el estudio de medidas de riesgo y de soluciones a problemas de asignación de capital, en su capacidad para responder cuestiones prácticas en el ámbito de las instituciones aseguradoras y financieras, y en su conexión con una familia de funciones denominadas operadores de agregación. Estos operadores son bien conocidos entre los investigadores de las comunidades de las ciencias de la información o de los conjuntos y sistemas fuzzy. La primera contribución de esta tesis es la introducción de las medidas de riesgo GlueVaR, una familia que pertenece a la clase más general de las medidas de riesgo de distorsión. Las medidas de riesgo GlueVaR son sencillas de entender para los gestores de riesgo de los sectores financiero y asegurador, puesto que están basadas en las medidas de riesgo más populares (el VaR y el TVaR) de ambas industrias. Por el mismo motivo, son casi tan fáciles de calcular como estas medidas de riesgo más comunes pero, además, las medidas de riesgo GlueVaR permiten capturar actitudes de gestión y regulatorias ante el riesgo más complicadas. La definición de la propiedad de la subadditividad en colas para un par de riesgos se puede considerar la segunda contribución. Una medida de riesgo de distorsión que cumple esta propiedad tiene la capacidad de ser subadditiva en escenarios extremadamente adversos. Con el propósito de decidir si una medida de riesgo GlueVaR es candidata a satisfacer la propiedad de la subadditividad en colas se determinan condiciones sobre sus parámetros. Se muestra que las medidas de riesgo de distorsión y varios operadores de medias ponderadas ordenadas en el caso finito y discreto están matemáticamente relacionadas a través de la integral de Choquet. Se muestra que la preferencia global de agregación del experto puede medirse usando el nivel local de orness de la medida de riesgo de distorsión, que es un concepto trasladado des de la comunidad de las ciencias de la información hacia la comunidad de la gestión cuantitativa del riesgo. Nuevos indicadores para ayudar a caracterizar las integrales de Choquet en el caso discreto también se presentan en esta disertación. Se pretende complementar a los existentes, con el fin de ser capaces de destacar características particulares de este tipo de funciones de agregación. Con este espíritu, se presentan el nivel de balance, la divergencia, el indicador de varianza y las entropías de Rényi como indicadores en el ámbito de la integral de Choquet. Una contribución relevante que se deriva de la relación entre las medidas de riesgo de distorsión y los operadores de agregación es la caracterización de la actitud ante el riesgo implícita en la elección de una medida de riesgo de distorsión y de un nivel de confianza. Se señala que la actitud ante el riesgo implícita en una medida de riesgo de distorsión está contenida, hasta cierto punto, en su función de distorsión. Para describir algunos rasgos relevantes de la función de distorsión se usan el indicador nivel de orness y una función cociente. Se muestra que estos instrumentos matemáticos aportan información relativa al comportamiento ante el riesgo implícito en las medidas de riesgo, y que de ellos se derivan las definiciones de les actitudes ante el riego de tipo general, absoluto y específico. En cuanto a los problemas de asignación 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 útiles como otras alternativas tales como el VaR o el TVaR para resolver problemas de asignación de capital. La segunda contribución consiste en entender los principios de asignación de capital como datos composicionales. Esta interpretación de los principios de asignación de capital permite establecer conexión entre los operadores de agregación y los problemas de asignación de capital, con una aplicación práctica inmediata: calcular debidamente la media de diferentes soluciones disponibles para el mismo problema de asignación de capital. Esta tesis contiene algunas ideas preliminares sobre esta conexión, pero parece un campo de investigación prometedor

Journal of Telecommunications and Information Technology, 2008, nr 4

kwartalni

Journal of Telecommunications and Information Technology, 2009, nr 3

kwartalni

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

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

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches