A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences

A multi-attribute decision making procedure using fuzzy numbers and hybrid aggregators

The classical Analytical Hierarchy Process (AHP) has two limitations. Firstly, it disregards the aspect of uncertainty that usually embedded in the data or information expressed by human. Secondly, it ignores the aspect of interdependencies among attributes during aggregation. The application of fuzzy numbers aids in confronting the former issue whereas, the usage of Choquet Integral operator helps in dealing with the later issue. However, the application of fuzzy numbers into multi-attribute decision making (MADM) demands some additional steps and inputs from decision maker(s). Similarly, identification of monotone measure weights prior to employing Choquet Integral requires huge number of computational steps and amount of inputs from decision makers, especially with the increasing number of attributes. Therefore, this research proposed a MADM procedure which able to reduce the number of computational steps and amount of information required from the decision makers when dealing with these two aspects simultaneously. To attain primary goal of this research, five phases were executed. First, the concept of fuzzy set theory and its application in AHP were investigated. Second, an analysis on the aggregation operators was conducted. Third, the investigation was narrowed on Choquet Integral and its associate monotone measure. Subsequently, the proposed procedure was developed with the convergence of five major components namely Factor Analysis, Fuzzy-Linguistic Estimator, Choquet Integral, Mikhailov‘s Fuzzy AHP, and Simple Weighted Average. Finally, the feasibility of the proposed procedure was verified by solving a real MADM problem where the image of three stores located in Sabak Bernam, Selangor, Malaysia was analysed from the homemakers‘ perspective. This research has a potential in motivating more decision makers to simultaneously include uncertainties in human‘s data and interdependencies among attributes when solving any MADM problems

Development of Machine Learning Techniques for Diabetic Retinopathy Risk Estimation

La retinopatia diabètica (DR) és una malaltia crònica. És una de les principals complicacions de diabetis i una causa essencial de pèrdua de visió entre les persones que pateixen diabetis. Els pacients diabètics han de ser analitzats periòdicament per tal de detectar signes de desenvolupament de la retinopatia en una fase inicial. El cribratge precoç i freqüent disminueix el risc de pèrdua de visió i minimitza la càrrega als centres assistencials. El nombre dels pacients diabètics està en augment i creixements ràpids, de manera que el fa difícil que consumeix recursos per realitzar un cribatge anual a tots ells. L’objectiu principal d’aquest doctorat. la tesi consisteix en construir un sistema de suport de decisions clíniques (CDSS) basat en dades de registre de salut electrònic (EHR). S'utilitzarà aquest CDSS per estimar el risc de desenvolupar RD. En aquesta tesi doctoral s'estudien mètodes d'aprenentatge automàtic per constuir un CDSS basat en regles lingüístiques difuses. El coneixement expressat en aquest tipus de regles facilita que el metge sàpiga quines combindacions de les condicions són les poden provocar el risc de desenvolupar RD. En aquest treball, proposo un mètode per reduir la incertesa en la classificació dels pacients que utilitzen arbres de decisió difusos (FDT). A continuació es combinen diferents arbres, usant la tècnica de Fuzzy Random Forest per millorar la qualitat de la predicció. A continuació es proposen diverses tècniques d'agregació que millorin la fusió dels resultats que ens dóna cadascun dels arbres FDT. Per millorar la decisió final dels nostres models, proposo tres mesures difuses que s'utilitzen amb integrals de Choquet i Sugeno. La definició d’aquestes mesures difuses es basa en els valors de confiança de les regles. En particular, una d'elles és una mesura difusa que es troba en la qual l'estructura jeràrquica de la FDT és explotada per trobar els valors de la mesura difusa. El resultat final de la recerca feta ha donat lloc a un programari que es pot instal·lar en centres d’assistència primària i hospitals, i pot ser usat pels metges de capçalera per fer l'avaluació preventiva i el cribatge de la Retinopatia Diabètica.La retinopatía diabética (RD) es una enfermedad crónica. Es una de las principales complicaciones de diabetes y una causa esencial de pérdida de visión entre las personas que padecen diabetes. Los pacientes diabéticos deben ser examinados periódicamente para detectar signos de diabetes. desarrollo de retinopatía en una etapa temprana. La detección temprana y frecuente disminuye el riesgo de pérdida de visión y minimiza la carga en los centros de salud. El número de pacientes diabéticos es enorme y está aumentando rápidamente, lo que lo hace difícil y Consume recursos para realizar una evaluación anual para todos ellos. El objetivo principal de esta tesis es construir un sistema de apoyo a la decisión clínica (CDSS) basado en datos de registros de salud electrónicos (EHR). Este CDSS será utilizado para estimar el riesgo de desarrollar RD. En este tesis doctoral se estudian métodos de aprendizaje automático para construir un CDSS basado en reglas lingüísticas difusas. El conocimiento expresado en este tipo de reglas facilita que el médico pueda saber que combinaciones de las condiciones son las que pueden provocar el riesgo de desarrollar RD. En este trabajo propongo un método para reducir la incertidumbre en la clasificación de los pacientes que usan árboles de decisión difusos (FDT). A continuación se combinan diferentes árboles usando la técnica de Fuzzy Random Forest para mejorar la calidad de la predicción. Se proponen también varias políticas para fusionar los resultados de que nos da cada uno de los árboles (FDT). Para mejorar la decisión final propongo tres medidas difusas que se usan con las integrales Choquet y Sugeno. La definición de estas medidas difusas se basa en los valores de confianza de las reglas. En particular, uno de ellos es una medida difusa descomponible en la que se usa la estructura jerárquica del FDT para encontrar los valores de la medida difusa. Como resultado final de la investigación se ha construido un software que puede instalarse en centros de atención médica y hospitales, i que puede ser usado por los médicos de cabecera para hacer la evaluación preventiva y el cribado de la Retinopatía Diabética.Diabetic retinopathy (DR) is a chronic illness. It is one of the main complications of diabetes, and an essential cause of vision loss among people suffering from diabetes. Diabetic patients must be periodically screened in order to detect signs of diabetic retinopathy development in an early stage. Early and frequent screening decreases the risk of vision loss and minimizes the load on the health care centres. The number of the diabetic patients is huge and rapidly increasing so that makes it hard and resource-consuming to perform a yearly screening to all of them. The main goal of this Ph.D. thesis is to build a clinical decision support system (CDSS) based on electronic health record (EHR) data. This CDSS will be utilised to estimate the risk of developing RD. In this Ph.D. thesis, I focus on developing novel interpretable machine learning systems. Fuzzy based systems with linguistic terms are going to be proposed. The output of such systems makes the physician know what combinations of the features that can cause the risk of developing DR. In this work, I propose a method to reduce the uncertainty in classifying diabetic patients using fuzzy decision trees. A Fuzzy Random forest (FRF) approach is proposed as well to estimate the risk for developing DR. Several policies are going to be proposed to merge the classification results achieved by different Fuzzy Decision Trees (FDT) models to improve the quality of the final decision of our models, I propose three fuzzy measures that are used with Choquet and Sugeno integrals. The definition of these fuzzy measures is based on the confidence values of the rules. In particular, one of them is a decomposable fuzzy measure in which the hierarchical structure of the FDT is exploited to find the values of the fuzzy measure. Out of this Ph.D. work, we have built a CDSS software that may be installed in the health care centres and hospitals in order to evaluate and detect Diabetic Retinopathy at early stages

EXPLAINABLE FEATURE- AND DECISION-LEVEL FUSION

Information fusion is the process of aggregating knowledge from multiple data sources to produce more consistent, accurate, and useful information than any one individual source can provide. In general, there are three primary sources of data/information: humans, algorithms, and sensors. Typically, objective data---e.g., measurements---arise from sensors. Using these data sources, applications such as computer vision and remote sensing have long been applying fusion at different levels (signal, feature, decision, etc.). Furthermore, the daily advancement in engineering technologies like smart cars, which operate in complex and dynamic environments using multiple sensors, are raising both the demand for and complexity of fusion. There is a great need to discover new theories to combine and analyze heterogeneous data arising from one or more sources. The work collected in this dissertation addresses the problem of feature- and decision-level fusion. Specifically, this work focuses on fuzzy choquet integral (ChI)-based data fusion methods. Most mathematical approaches for data fusion have focused on combining inputs relative to the assumption of independence between them. However, often there are rich interactions (e.g., correlations) between inputs that should be exploited. The ChI is a powerful aggregation tool that is capable modeling these interactions. Consider the fusion of m sources, where there are 2m unique subsets (interactions); the ChI is capable of learning the worth of each of these possible source subsets. However, the complexity of fuzzy integral-based methods grows quickly, as the number of trainable parameters for the fusion of m sources scales as 2m. Hence, we require a large amount of training data to avoid the problem of over-fitting. This work addresses the over-fitting problem of ChI-based data fusion with novel regularization strategies. These regularization strategies alleviate the issue of over-fitting while training with limited data and also enable the user to consciously push the learned methods to take a predefined, or perhaps known, structure. Also, the existing methods for training the ChI for decision- and feature-level data fusion involve quadratic programming (QP). The QP-based learning approach for learning ChI-based data fusion solutions has a high space complexity. This has limited the practical application of ChI-based data fusion methods to six or fewer input sources. To address the space complexity issue, this work introduces an online training algorithm for learning ChI. The online method is an iterative gradient descent approach that processes one observation at a time, enabling the applicability of ChI-based data fusion on higher dimensional data sets. In many real-world data fusion applications, it is imperative to have an explanation or interpretation. This may include providing information on what was learned, what is the worth of individual sources, why a decision was reached, what evidence process(es) were used, and what confidence does the system have on its decision. However, most existing machine learning solutions for data fusion are black boxes, e.g., deep learning. In this work, we designed methods and metrics that help with answering these questions of interpretation, and we also developed visualization methods that help users better understand the machine learning solution and its behavior for different instances of data

Fuzzy Operator Trees for Modeling Utility Functions

In this thesis, we propose a method for modeling utility (rating) functions based on a novel concept called textbf{Fuzzy Operator Tree} (FOT for short). As the notion suggests, this method makes use of techniques from fuzzy set theory and implements a fuzzy rating function, that is, a utility function that maps to the unit interval, where $0$ corresponds to the lowest and $1$ to the highest evaluation. Even though the original motivation comes from quality control, FOTs are completely general and widely applicable. Our approach allows a human expert to specify a model in the form of an FOT in a quite convenient and intuitive way. To this end, he simply has to split evaluation criteria into sub-criteria in a recursive manner, and to determine in which way these sub-criteria ought to be combined: conjunctively, disjunctively, or by means of an averaging operator. The result of this process is the qualitative structure of the model. A second step, then, it is to parameterize the model. To support or even free the expert form this step, we develop a method for calibrating the model on the basis of exemplary ratings, that is, in a purely data-driven way. This method, which makes use of optimization techniques from the field of evolutionary algorithms, constitutes the second major contribution of the thesis. The third contribution of the thesis is a method for evaluating an FOT in a cost-efficient way. Roughly speaking, an FOT can be seen as an aggregation function that combines the evaluations of a number of basic criteria into an overall rating of an object. Essentially, the cost of computing this rating is hence given by sum of the evaluation costs of the basic criteria. In practice, however, the precise utility degree is often not needed. Instead, it is enough to know whether it lies above or below an important threshold value. In such cases, the evaluation process, understood as a sequential evaluation of basic criteria, can be stopped as soon as this question can be answered in a unique way. Of course, the (expected) number of basic criteria and, therefore, the (expected) evaluation cost will then strongly depend on the order of the evaluations, and this is what is optimized by the methods that we have developed

North American Fuzzy Logic Processing Society (NAFIPS 1992), volume 2

This document contains papers presented at the NAFIPS '92 North American Fuzzy Information Processing Society Conference. More than 75 papers were presented at this Conference, which was sponsored by NAFIPS in cooperation with NASA, the Instituto Tecnologico de Morelia, the Indian Society for Fuzzy Mathematics and Information Processing (ISFUMIP), the Instituto Tecnologico de Estudios Superiores de Monterrey (ITESM), the International Fuzzy Systems Association (IFSA), the Japan Society for Fuzzy Theory and Systems, and the Microelectronics and Computer Technology Corporation (MCC). The fuzzy set theory has led to a large number of diverse applications. Recently, interesting applications have been developed which involve the integration of fuzzy systems with adaptive processes such a neural networks and genetic algorithms. NAFIPS '92 was directed toward the advancement, commercialization, and engineering development of these technologies

Advanced Fault Diagnosis and Health Monitoring Techniques for Complex Engineering Systems

Over the last few decades, the field of fault diagnostics and structural health management has been experiencing rapid developments. The reliability, availability, and safety of engineering systems can be significantly improved by implementing multifaceted strategies of in situ diagnostics and prognostics. With the development of intelligence algorithms, smart sensors, and advanced data collection and modeling techniques, this challenging research area has been receiving ever-increasing attention in both fundamental research and engineering applications. This has been strongly supported by the extensive applications ranging from aerospace, automotive, transport, manufacturing, and processing industries to defense and infrastructure industries