A weighted goal programming approach to fuzzy linear regression with quasi type-2 fuzzy input-output data

This study attempts to develop a regression model when both input data and output data are quasi type-2 fuzzy numbers. To estimate the crisp parameters of the regression model, a linear programming model is proposed based on goal programming. To handle the outlier problem, an omission approach is proposed. This approach examines the behavior of value changes in the objective function of proposed model when observations are omitted. In order to illustrate the proposed model, some numerical examples are presented. The applicability of the proposed method is tested on a real data set on soil science. The predictive performance of the model is examined by cross-validation.Publisher's Versio

A novel framework for predicting patients at risk of readmission

Uncertainty in decision-making for patients’ risk of re-admission arises due to non-uniform data and lack of knowledge in health system variables. The knowledge of the impact of risk factors will provide clinicians better decision-making and in reducing the number of patients admitted to the hospital. Traditional approaches are not capable to account for the uncertain nature of risk of hospital re-admissions. More problems arise due to large amount of uncertain information. Patients can be at high, medium or low risk of re-admission, and these strata have ill-defined boundaries. We believe that our model that adapts fuzzy regression method will start a novel approach to handle uncertain data, uncertain relationships between health system variables and the risk of re-admission. Because of nature of ill-defined boundaries of risk bands, this approach does allow the clinicians to target individuals at boundaries. Targeting individuals at boundaries and providing them proper care may provide some ability to move patients from high risk to low risk band. In developing this algorithm, we aimed to help potential users to assess the patients for various risk score thresholds and avoid readmission of high risk patients with proper interventions. A model for predicting patients at high risk of re-admission will enable interventions to be targeted before costs have been incurred and health status have deteriorated. A risk score cut off level would flag patients and result in net savings where intervention costs are much higher per patient. Preventing hospital re-admissions is important for patients, and our algorithm may also impact hospital income

Estimación Borrosa del Riesgo Beta. Análisis Comparativo

Aquesta tesi representa una aportació a la literatura empírica sobre el risc sistemàtic a nivell sectorial en mercats emergents llatinoamericans, en calcular betes borroses, sectorials i individuals, de Xile, Brasil i Mèxic, i comparar el seu comportament amb el de les betes d’alguns països desenvolupats com Estats Units, Regne Unit i Japó. Proposem una representació borrosa del model de mercat que incorpora el càlcul del rendiment d’un actiu expressat a través d’un interval de confiança. D’aquesta manera incorporem en el càlcul de la beta tota la informació disponible de les cotitzacions d’un actiu durant el dia. Com a resultat de l’estimació amb aquest model obtenim un coeficient beta borrós. Comencem l’estudi comparant i avaluant els resultats obtinguts segons s’expressi la rendibilitat dels actius i segons els diferents mètodes d’estimació de la beta, MCO i regressió borrosa lineal de Tanaka i Ishibuchi (1992) millorada amb el mètode de detecció d’outliers de Hung i Yang (2006). Finalment, avancem en l’estudi de la beta borrosa com a indicador del risc sistemàtic. Proposem una classificació dels actius basada en la beta borrosa i verifiquem si dues de les hipòtesis tradicionals de la teoria de carteres es compleixen en un entorn d’incertesa: i) la beta sectorial presenta major estabilitat que la beta individual; ii) com més gran és el període d’estimació, major és l’estabilitat de la beta.Esta tesis representa un aporte a la literatura empírica sobre el riesgo sistemático a nivel sectorial en mercados emergentes latinoamericanos, al calcular betas borrosas, sectoriales e individuales, en Chile, Brasil y Méjico y comparar su comportamiento con él de las betas de algunos países desarrollados como Estados Unidos, Reino Unido y Japón. Proponemos una representación borrosa del modelo de mercado que incorpora el cálculo del rendimiento de un activo expresado a través de un intervalo de confianza. Con ello incorporamos en el cálculo de la beta toda la información disponible de las cotizaciones de un activo durante el día. Como resultado de la estimación con dicho modelo obtenemos un coeficiente beta borroso. Comenzamos el estudio comparando y evaluando los resultados obtenidos según se exprese la rentabilidad de los activos y según los diferentes métodos de estimación de la beta, MCO y regresión borrosa lineal de Tanaka e Ishibuchi (1992) mejorada con el método de detección de outliers de Hung y Yang (2006). Por último, avanzamos en el estudio de la beta borrosa como indicador del riesgo sistemático. Proponemos una nueva clasificación de los activos basada en la beta borrosa y verificamos si dos de las hipótesis tradicionales de la teoría de carteras se cumplen en un entorno de incertidumbre: i) la beta sectorial presenta mayor estabilidad que la beta individual; ii) Cuánto mayor es el período de estimación, mayor es la estabilidad de la beta.This thesis represents a contribution to empirical literature on systematic risk at the sectoral level in Latin American emerging markets, by calculating fuzzy betas, sectoral and individual, in Chile, Brazil and Mexico, and to compare its behavior with that of betas in some developed countries as the United States, the United Kingdom and Japan. We propose a fuzzy representation of the model of market that incorporates the calculation of the return of an asset expressed through a confidence interval. With it we incorporate in the calculation of the beta all the information available of the quotation of an asset during the day. As a result of the estimation with that model we obtain a fuzzy beta coefficient. We begin the study by comparing and evaluating the results obtained according to assets return and to the different beta methods of estimation, MCO and lineal fuzzy regression of Tanaka e Ishibuchi (1992) improved with the detection of outliers model of the Hung and Yung (2006). Finally, we advance in the study of fuzzy beta as an indicator of systematic risk. We propose a classification of assets based on fuzzy beta and we verify if two of the traditional hypotheses of the portfolio theory are met in an uncertainty environment: i) sectoral beta shows greater stability than individual beta; ii) the longer the estimation period is, the greater the stability of the bet