Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers

The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources. However, there are many problems where this information is unavailable, such as crowdsourcing. This paper focuses on data-informed FMs, or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data they provide. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. This paper extends upon our previous work in datainformed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. We then extend data-informed FMs to fuzzy number (FN)-valued inputs. We demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data

Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multi-layer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy and our previously established XAI indices shed light on the quality of our data, model, and its decisions.Comment: IEEE Transactions on Fuzzy System

Spatial modelling of adaptation strategies for urban built infrastructures exposed to flood hazards

The recent 2010/2011 floods in the central and southern Queensland (Australia) prompted this research to investigate the application of geographical information system (GIS) and remote sensing in modelling the current flood risk, adaptation/coping capacity, and adaptation strategies. Identified Brisbane City as the study area, the study aimed to develop a new approach of formulating adaptation/coping strategies that will aid in addressing flood risk management issues of an urban area with intensive residential and commercial uses. Fuzzy logic was the spatial analytical tool used in the integration of flood risk components (hazard, vulnerability, and exposure) and in the generation of flood risk and adaptation capacity indices. The research shows that 875 ha, 566 ha, and 828 ha were described as areas with relatively low, relatively moderate, and relatively high risk to flooding, respectively. Identified adaptation strategies for areas classified as having relatively low (RL), relatively moderate (RM), relatively high (RH), and likely very high (LVH) adaptation/coping capacity were mitigation to recovery phases, mitigation to response phases, mitigation to preparedness phases, and mitigation phase, respectively. Integrating the results from the flood risk assessment, quantitative description of adaptation capacity, and identification of adaptation strategies, a new analytical technique identified as flood risk-adaptation capacity index-adaptation strategies (FRACIAS) linkage model was developed for this study

Novel similarity measure for interval-valued data based on overlapping ratio

In computing the similarity of intervals, current similarity measures such as the commonly used Jaccard and Dice measures are at times not sensitive to changes in the width of intervals, producing equal similarities for substantially different pairs of intervals. To address this, we propose a new similarity measure that uses a bi-directional approach to determine interval similarity. For each direction, the overlapping ratio of the given interval in a pair with the other interval is used as a measure of uni-directional similarity. We show that the proposed measure satisfies all common properties of a similarity measure, while also being invariant in respect to multiplication of the interval endpoints and exhibiting linear growth in respect to linearly increasing overlap. Further, we compare the behavior of the proposed measure with the highly popular Jaccard and Dice similarity measures, highlighting that the proposed approach is more sensitive to changes in interval widths. Finally, we show that the proposed similarity is bounded by the Jaccard and the Dice similarity, thus providing a reliable alternative

A proposed framework for characterising uncertainty and variability in rock mechanics and rock engineering

This thesis develops a novel understanding of the fundamental issues in characterising and propagating unpredictability in rock engineering design. This unpredictability stems from the inherent complexity and heterogeneity of fractured rock masses as engineering media. It establishes the importance of: a) recognising that unpredictability results from epistemic uncertainty (i.e. resulting from a lack of knowledge) and aleatory variability (i.e. due to inherent randomness), and; b) the means by which uncertainty and variability associated with the parameters that characterise fractured rock masses are propagated through the modelling and design process. Through a critical review of the literature, this thesis shows that in geotechnical engineering – rock mechanics and rock engineering in particular – there is a lack of recognition in the existence of epistemic uncertainty and aleatory variability, and hence inappropriate design methods are often used. To overcome this, a novel taxonomy is developed and presented that facilitates characterisation of epistemic uncertainty and aleatory variability in the context of rock mechanics and rock engineering. Using this taxonomy, a new framework is developed that gives a protocol for correctly propagating uncertainty and variability through engineering calculations. The effectiveness of the taxonomy and the framework are demonstrated through their application to simple challenge problems commonly found in rock engineering. This new taxonomy and framework will provide engineers engaged in preparing rock engineering designs an objective means of characterising unpredictability in parameters commonly used to define properties of fractured rock masses. These new tools will also provide engineers with a means of clearly understanding the true nature of unpredictability inherent in rock mechanics and rock engineering, and thus direct selection of an appropriate unpredictability model to propagate unpredictability faithfully through engineering calculations. Thus, the taxonomy and framework developed in this thesis provide practical tools to improve the safety of rock engineering designs through an improved understanding of the unpredictability concepts.Open Acces

SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence

Information or data aggregation is an important part of nearly all analysis problems as summarizing inputs from multiple sources is a ubiquitous goal. In this paper we propose a method for non-linear aggregation of data inputs that take the form of non-normal fuzzy sets. The proposed shape-preserving fuzzy integral (SPFI) is designed to overcome a well-known weakness of the previously-proposed sub-normal fuzzy integral (SuFI). The weakness of SuFI is that the output is constrained to have maximum membership equal to the minimum of the maximum memberships of the inputs; hence, if one input has a small height, then the output is constrained to that height. The proposed SPFI does not suffer from this weakness and, furthermore, preserves in the output the shape of the input sets. That is, the output looks like the inputs. The SPFI method is based on the well-known Choquet fuzzy integral with respect to a capacity measure, i.e., fuzzy measure. We demonstrate SPFI on synthetic and real-world data, comparing it to the SuFI and non-direct fuzzy integral (NDFI)

Soft computing approaches to uncertainty propagation in environmental risk mangement

Real-world problems, especially those that involve natural systems, are complex and composed of many nondeterministic components having non-linear coupling. It turns out that in dealing with such systems, one has to face a high degree of uncertainty and tolerate imprecision. Classical system models based on numerical analysis, crisp logic or binary logic have characteristics of precision and categoricity and classified as hard computing approach. In contrast soft computing approaches like probabilistic reasoning, fuzzy logic, artificial neural nets etc have characteristics of approximation and dispositionality. Although in hard computing, imprecision and uncertainty are undesirable properties, in soft computing the tolerance for imprecision and uncertainty is exploited to achieve tractability, lower cost of computation, effective communication and high Machine Intelligence Quotient (MIQ). Proposed thesis has tried to explore use of different soft computing approaches to handle uncertainty in environmental risk management. The work has been divided into three parts consisting five papers. In the first part of this thesis different uncertainty propagation methods have been investigated. The first methodology is generalized fuzzy α-cut based on the concept of transformation method. A case study of uncertainty analysis of pollutant transport in the subsurface has been used to show the utility of this approach. This approach shows superiority over conventional methods of uncertainty modelling. A Second method is proposed to manage uncertainty and variability together in risk models. The new hybrid approach combining probabilistic and fuzzy set theory is called Fuzzy Latin Hypercube Sampling (FLHS). An important property of this method is its ability to separate randomness and imprecision to increase the quality of information. A fuzzified statistical summary of the model results gives indices of sensitivity and uncertainty that relate the effects of variability and uncertainty of input variables to model predictions. The feasibility of the method is validated to analyze total variance in the calculation of incremental lifetime risks due to polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) for the residents living in the surroundings of a municipal solid waste incinerator (MSWI) in Basque Country, Spain. The second part of this thesis deals with the use of artificial intelligence technique for generating environmental indices. The first paper focused on the development of a Hazzard Index (HI) using persistence, bioaccumulation and toxicity properties of a large number of organic and inorganic pollutants. For deriving this index, Self-Organizing Maps (SOM) has been used which provided a hazard ranking for each compound. Subsequently, an Integral Risk Index was developed taking into account the HI and the concentrations of all pollutants in soil samples collected in the target area. Finally, a risk map was elaborated by representing the spatial distribution of the Integral Risk Index with a Geographic Information System (GIS). The second paper is an improvement of the first work. New approach called Neuro-Probabilistic HI was developed by combining SOM and Monte-Carlo analysis. It considers uncertainty associated with contaminants characteristic values. This new index seems to be an adequate tool to be taken into account in risk assessment processes. In both study, the methods have been validated through its implementation in the industrial chemical / petrochemical area of Tarragona. The third part of this thesis deals with decision-making framework for environmental risk management. In this study, an integrated fuzzy relation analysis (IFRA) model is proposed for risk assessment involving multiple criteria. The fuzzy risk-analysis model is proposed to comprehensively evaluate all risks associated with contaminated systems resulting from more than one toxic chemical. The model is an integrated view on uncertainty techniques based on multi-valued mappings, fuzzy relations and fuzzy analytical hierarchical process. Integration of system simulation and risk analysis using fuzzy approach allowed to incorporate system modelling uncertainty and subjective risk criteria. In this study, it has been shown that a broad integration of fuzzy system simulation and fuzzy risk analysis is possible. In conclusion, this study has broadly demonstrated the usefulness of soft computing approaches in environmental risk analysis. The proposed methods could significantly advance practice of risk analysis by effectively addressing critical issues of uncertainty propagation problem.Los problemas del mundo real, especialmente aquellos que implican sistemas naturales, son complejos y se componen de muchos componentes indeterminados, que muestran en muchos casos una relación no lineal. Los modelos convencionales basados en técnicas analíticas que se utilizan actualmente para conocer y predecir el comportamiento de dichos sistemas pueden ser muy complicados e inflexibles cuando se quiere hacer frente a la imprecisión y la complejidad del sistema en un mundo real. El tratamiento de dichos sistemas, supone el enfrentarse a un elevado nivel de incertidumbre así como considerar la imprecisión. Los modelos clásicos basados en análisis numéricos, lógica de valores exactos o binarios, se caracterizan por su precisión y categorización y son clasificados como una aproximación al hard computing. Por el contrario, el soft computing tal como la lógica de razonamiento probabilístico, las redes neuronales artificiales, etc., tienen la característica de aproximación y disponibilidad. Aunque en la hard computing, la imprecisión y la incertidumbre son propiedades no deseadas, en el soft computing la tolerancia en la imprecisión y la incerteza se aprovechan para alcanzar tratabilidad, bajos costes de computación, una comunicación efectiva y un elevado Machine Intelligence Quotient (MIQ). La tesis propuesta intenta explorar el uso de las diferentes aproximaciones en la informática blanda para manipular la incertidumbre en la gestión del riesgo medioambiental. El trabajo se ha dividido en tres secciones que forman parte de cinco artículos. En la primera parte de esta tesis, se han investigado diferentes métodos de propagación de la incertidumbre. El primer método es el generalizado fuzzy α-cut, el cual está basada en el método de transformación. Para demostrar la utilidad de esta aproximación, se ha utilizado un caso de estudio de análisis de incertidumbre en el transporte de la contaminación en suelo. Esta aproximación muestra una superioridad frente a los métodos convencionales de modelación de la incertidumbre. La segunda metodología propuesta trabaja conjuntamente la variabilidad y la incertidumbre en los modelos de evaluación de riesgo. Para ello, se ha elaborado una nueva aproximación híbrida denominada Fuzzy Latin Hypercube Sampling (FLHS), que combina los conjuntos de la teoría de probabilidad con la teoría de los conjuntos difusos. Una propiedad importante de esta teoría es su capacidad para separarse los aleatoriedad y imprecisión, lo que supone la obtención de una mayor calidad de la información. El resumen estadístico fuzzificado de los resultados del modelo generan índices de sensitividad e incertidumbre que relacionan los efectos de la variabilidad e incertidumbre de los parámetros de modelo con las predicciones de los modelos. La viabilidad del método se llevó a cabo mediante la aplicación de un caso a estudio donde se analizó la varianza total en la cálculo del incremento del riesgo sobre el tiempo de vida de los habitantes que habitan en los alrededores de una incineradora de residuos sólidos urbanos en Tarragona, España, debido a las emisiones de dioxinas y furanos (PCDD/Fs). La segunda parte de la tesis consistió en la utilización de las técnicas de la inteligencia artificial para la generación de índices medioambientales. En el primer artículo se desarrolló un Índice de Peligrosidad a partir de los valores de persistencia, bioacumulación y toxicidad de un elevado número de contaminantes orgánicos e inorgánicos. Para su elaboración, se utilizaron los Mapas de Auto-Organizativos (SOM), que proporcionaron un ranking de peligrosidad para cada compuesto. A continuación, se elaboró un Índice de Riesgo Integral teniendo en cuenta el Índice de peligrosidad y las concentraciones de cada uno de los contaminantes en las muestras de suelo recogidas en la zona de estudio. Finalmente, se elaboró un mapa de la distribución espacial del Índice de Riesgo Integral mediante la representación en un Sistema de Información Geográfico (SIG). El segundo artículo es un mejoramiento del primer trabajo. En este estudio, se creó un método híbrido de los Mapas Auto-organizativos con los métodos probabilísticos, obteniéndose de esta forma un Índice de Riesgo Integrado. Mediante la combinación de SOM y el análisis de Monte-Carlo se desarrolló una nueva aproximación llamada Índice de Peligrosidad Neuro-Probabilística. Este nuevo índice es una herramienta adecuada para ser utilizada en los procesos de análisis. En ambos artículos, la viabilidad de los métodos han sido validados a través de su aplicación en el área de la industria química y petroquímica de Tarragona (Cataluña, España). El tercer apartado de esta tesis está enfocado en la elaboración de una estructura metodológica de un sistema de ayuda en la toma de decisiones para la gestión del riesgo medioambiental. En este estudio, se presenta un modelo integrado de análisis de fuzzy (IFRA) para la evaluación del riesgo cuyo resultado depende de múltiples criterios. El modelo es una visión integrada de las técnicas de incertidumbre basadas en diseños de valoraciones múltiples, relaciones fuzzy y procesos analíticos jerárquicos inciertos. La integración de la simulación del sistema y el análisis del riesgo utilizando aproximaciones inciertas permitieron incorporar la incertidumbre procedente del modelo junto con la incertidumbre procedente de la subjetividad de los criterios. En este estudio, se ha demostrado que es posible crear una amplia integración entre la simulación de un sistema incierto y de un análisis de riesgo incierto. En conclusión, este trabajo demuestra ampliamente la utilidad de aproximación Soft Computing en el análisis de riesgos ambientales. Los métodos propuestos podría avanzar significativamente la práctica de análisis de riesgos de abordar eficazmente el problema de propagación de incertidumbre

Keystroke dynamics in the pre-touchscreen era

Biometric authentication seeks to measure an individual’s unique physiological attributes for the purpose of identity verification. Conventionally, this task has been realized via analyses of fingerprints or signature iris patterns. However, whilst such methods effectively offer a superior security protocol compared with password-based approaches for example, their substantial infrastructure costs, and intrusive nature, make them undesirable and indeed impractical for many scenarios. An alternative approach seeks to develop similarly robust screening protocols through analysis of typing patterns, formally known as keystroke dynamics. Here, keystroke analysis methodologies can utilize multiple variables, and a range of mathematical techniques, in order to extract individuals’ typing signatures. Such variables may include measurement of the period between key presses, and/or releases, or even key-strike pressures. Statistical methods, neural networks, and fuzzy logic have often formed the basis for quantitative analysis on the data gathered, typically from conventional computer keyboards. Extension to more recent technologies such as numerical keypads and touch-screen devices is in its infancy, but obviously important as such devices grow in popularity. Here, we review the state of knowledge pertaining to authentication via conventional keyboards with a view toward indicating how this platform of knowledge can be exploited and extended into the newly emergent type-based technological contexts