
Christian WagnerUniversity of Nottingham | Notts · School of Computer Science
Christian Wagner
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Publications (214)
The rules of a rule-based system provide explanations for its behaviour by revealing the relationships between the variables captured. However, ideally, we have AI systems which go beyond explainable AI (XAI), that is, systems which not only explain their behaviour, but also communicate their ‘insights’ in respect to the real world. This requires r...
Since their introduction, fuzzy sets and systems have become an important area of research known for its versatility in modelling, knowledge representation and reasoning, and increasingly its potential within the context explainable AI. While the applications of fuzzy systems are diverse, there has been comparatively little advancement in their des...
Hierarchical fuzzy systems (HFSs) are claimed to be an excellent approach to reducing the number of rules in Fuzzy logic systems (FLSs). Further, HFSs have also been shown to have the potential to reduce complexity and improve interpretability for FLSs. However, designing an interpretable HFS is a challenging task. This is due to the HFSs' structur...
Deformable image registration (alignment) is highly sought after in numerous clinical applications, such as computer aided diagnosis and disease progression analysis. Deep Convolutional Neural Network (DCNN)-based image registration methods have demonstrated advantages in terms of registration accuracy and computational speed. However, while most m...
Hierarchical Fuzzy Systems (HFSs) have been viewed as a promising option to overcoming a fundamental problem in Fuzzy Logic Systems (FLSs), namely the rule explosion associated with an increase in input variables. In HFSs, the original FLS is decomposed into a number of low-dimensional fuzzy logic subsystems. As a result, rules in HFSs typically ha...
Most of statistics and AI draw insights through modelling discord or variance between sources (i.e., inter-source) of information. Increasingly however, research is focusing on uncertainty arising at the level of individual measurements (i.e., within- or intra-source), such as for a given sensor output or human response. Here, adopting intervals ra...
Commercial driving is a complex multifaceted task influenced by drivers' personal traits and external contextual factors, such as weather, traffic, and road conditions. Current intelligent commercial driving assessment systems only focus on the manner by which drivers operate vehicle controls when analysing driving performance and the impact of dri...
Economists have sought to predict stock market prices for decades with varying degrees of success. This study classifies stocks according to their stability in two consequent financial quarters (depending on whether the majority of stocks remain in the same stability group, which can indicate forecastability). However, classifying temporal informat...
Economists have sought to predict stock market prices for decades with varying degrees of success. This study classifies stocks according to their stability in two consequent financial quarters (depending on whether the majority of stocks remain in the same stability group, which can indicate forecastability). However, classifying temporal informat...
There have been ongoing discussions in research communities, including the field of trustworthy autonomous systems (TAS), on how researchers may meaningfully engage with responsible research and innovation (RRI). By critically reflecting on the RRI aspects of an ongoing research project focussing on the efficient capture of richer quantitative huma...
Mango is the third most crucial fruit product worldwide in terms of value and production volume, after pineapple and banana. However, assessing the quality grading of mangoes
in an agricultural environment as a manual task is inefficient, labour demanding, and prone to errors. Thus, this task entails uncertainty in human decision-making, i.e. choic...
In this work we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence fun...
Data obtained from the real-world tends to be uncertain: Measurement inaccuracies, variability in opinions, and human errors are just some of the reasons that make the information collection process noisy. In recent years, fuzzy sets have been used to capture the uncertainty in data and then build automatic reasoning systems. In some contexts, data...
Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields. Traditional and ubiquitous response formats such as Likert and visual analogue scales require condensation of responses into discrete or point values—but sometimes a range of options may better represent the correct answer. In this p...
Brain age estimation based on magnetic resonance imaging (MRI) is an active research area in early diagnosis of some neurodegenerative diseases (e.g. Alzheimer, Parkinson, Huntington, etc.) for elderly people or brain underdevelopment for the young group. Deep learning methods have achieved the state-of-the-art performance in many medical image ana...
The use of Hierarchical Fuzzy Systems (HFS) has been well acknowledged as a good approach in reducing the complexity and improving the interpretability of fuzzy logic systems (FLS). Over the past years, many fuzzy logic toolkits have been made available for type-1, interval type-2 and general type-2 fuzzy logic systems under different programming l...
Brain age estimation based on magnetic resonance imaging (MRI) is an active research area in early diagnosis of some neurodegenerative diseases (e.g. Alzheimer, Parkinson, Huntington, etc.) for elderly people or brain underdevelopment for the young group. Deep learning methods have achieved the state-of-the-art performance in many medical image ana...
Regression represents one of the most basic building
blocks of data analysis and AI. Despite growing interest in
interval-valued data across various fields, approaches to establish
regression models for interval-valued data which address and
handle the specific properties of given data sets are very limited.
For broader use and adoption of regressi...
Capturing interval-valued, as opposed to more conventional point-valued data, offers a potentially efficient method of obtaining richer information in individual responses. In turn, interval-valued data provide a strong foundation for subsequent fuzzy set based modelling--e.g., using the Interval Agreement Approach. In 2019, open-source software (D...
Most of statistics and AI draw insights through modelling discord or variance between sources of information (i.e., inter-source uncertainty). Increasingly, however, research is focusing upon uncertainty arising at the level of individual measurements (i.e., within- or intra-source), such as for a given sensor output or human response. Here, adopti...
Quality of life assessment represents a key process of deciding treatment success and viability. As such, patients' perceptions of their functional status and well-being are important inputs for impairment assessment. Given that patient completed questionnaires are often used to assess patient status and determine future treatment options, it is im...
Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields (e.g. perceptual and categorical judgement, expert risk assessment, attitudinal measurement, consumer and public opinion research). Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensa...
Constrained interval type-2 (CIT2) fuzzy sets have been introduced to preserve interpretability when moving from type-1 (T1) to interval type-2 (IT2) membership functions. Although they can be used to produce type-2 fuzzy systems with enhanced explainability, so far, the latter comes at the expense of high computational cost. Specifically, the exha...
Interpretability is an important and necessary topic that needs to be discussed in relation to the fields of Artificial Intelligence and Machine Learning. Within fuzzy logic systems (FLSs), hierarchical fuzzy systems (HFSs) have been suggested as a key component to help improve the interpretability of FLSs. In this context, complexity is a key comp...
Recent advances in the literature have leveraged the fuzzy integral (FI), a powerful multi-source aggregation operator, where a fuzzy measure (FM) is used to capture the worth of all combinations of subsets of sources. While in most applications, the FM is defined either by experts or numerically derived through optimization, these approaches are o...
Fuzzy Logic Systems can provide a good level of interpretability and may provide a key building block as part of a growing interest in explainable AI. In practice, the level of interpretability of a given fuzzy logic system is dependent on how well its key components, namely, its rule base and its antecedent and consequent fuzzy sets are understood...
Deep learning based image segmentation has achieved the state-of-the-art performance in many medical applications such as lesion quantification, organ detection, etc. However, most of the methods rely on supervised learning, which require a large set of high-quality labeled data. Data annotation is generally an extremely time-consuming process. To...
Deep learning based image segmentation has achieved the state-of-the-art performance in many medical applications such as lesion quantification, organ detection, etc. However, most of the methods rely on supervised learning, which require a large set of high-quality labeled data. Data annotation is generally an extremely time-consuming process. To...
Fuzzy Logic Systems can provide a good level of interpretability and may provide a key building block as part of a growing interest in
explainable AI. In practice, the level of interpretability of a given fuzzy
logic system is dependent on how well its key components, namely, its rule base and its antecedent and consequent fuzzy sets are understood...
With a growing number of areas leveraging interval-valued data—including in the context of modelling human uncertainty (e.g., in Cyber Security), the capacity to accurately and systematically compare intervals for reasoning and computation is increasingly important. In practice, well established set-theoretic similarity measures such as the Jaccard...
Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve the interpretability of fuzzy logic systems (FLSs). However, challenges remain, such as: "How can we measure their interpretability?", "How can we make an informed assessment of how HFSs should be designed to enhance interpretability?". The challenges of measuring th...
This capsule demonstrates a general framework for an index to measure the interpretability of Hierarchical Fuzzy Systems
Subjective judgements from experts provide essential information when assessing and modelling threats in respect to cyber-physical systems. For example, the vulnerability of individual system components can be described using multiple factors, such as complexity, technological maturity, and the availability of tools to aid an attack. Such informati...
Subjective judgements from experts provide essential information when assessing and modelling threats in respect to cyber-physical systems. For example, the vulnerability of individual system components can be described using multiple factors, such as complexity, technological maturity, and the availability of tools to aid an attack. Such informati...
Similarity measures are among the most common methods of comparing type-2 fuzzy sets and have been used in numerous applications. However, deciding how to measure similarity and choosing which existing measure to use can be difficult. Whilst some measures give results that highly correlate with each other, others give considerably different results...
Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to capture and handle input noise within the design of input fuzzy sets. In this paper, we propose an online learning method which utilises a sequence of observations to continuously update the input Fuzzy Sets (FSs) of an NSFLS, thus providing an improved capacity to deal with variation...
Determining the driving styles and the factors causing incidents in real time could assist stakeholders to promote actions and develop feedback systems to reduce risks, costs and to increase safety in roads. This paper presents a classification system for Heavy Goods Vehicles (HGVs) drivers, using a core set of driving pattern stereotypes which wer...
Recently, there has been much research into modelling of uncertainty in human perception through Fuzzy Sets (FSs). Most of this research has focused on allowing respondents to express their (intra) uncertainty using intervals. Here, depending on the technique used and types of uncertainties being modelled different types of FSs can be obtained (e.g...
Purpose
Many transport and logistics companies nowadays use raw vehicle GPS data for travel time prediction. However, they face difficult challenges in terms of the costs of information storage, as well as the quality of the prediction. This paper aims to systematically investigate various meta-data (features) that require significantly less storag...
Data-driven techniques that capture uncertainty through intervals or fuzzy sets can substantially improve systematic reasoning about uncertain information. Recent years have seen renewed interest in the capture of intervals from a variety of sources-including experts and general survey participants. This approach avoids the more cumbersome batterie...
Aggregation operators are mathematical functions that enable the fusion of information from multiple sources. Fuzzy Integrals (FIs) are widely used aggregation operators, which combine information in respect to a Fuzzy Measure (FM) which captures the worth of both the individual sources and all their possible combinations. However, FIs suffer from...
Hierarchical fuzzy systems (HFSs) have been seen as an effective approach to reduce the complexity of fuzzy logic systems (FLSs), largely as a result of reducing the number of rules. However, it is not clear completely how complexity of HFSs can be measured. In FLSs, complexity is commonly expressed using a multi-factorial approach, taking into con...
Recently, there has been much research into modelling of uncertainty in human perception through Fuzzy Sets (FSs). Most of this research has focused on allowing respondents to express their (intra) uncertainty using intervals. Here, depending on the technique used and types of uncertainties being modelled different types of FSs can be obtained (e.g...
Comparing fuzzy sets by computing their similarity is common, with a large set of measures of similarity available. However, while commonplace in the computational intelligence community, the application and results of similarity measures are less common in the wider scientific context, where statistical approaches are the standard for comparing di...
Discontinuous intervals (DIs) arise in a wide range of contexts, from real world data capture of human opinion to α-cuts of non-convex fuzzy sets. Commonly, for assessing the similarity of DIs, the latter are converted into their continuous form, followed by the application of a continuous interval (CI) compatible similarity measure. While this con...
Scientific projects that require human computation often resort to crowdsourcing. Interested individuals can contribute to a crowdsourcing task, essentially contributing towards the project’s goals. To motivate participation and engagement, scientists use a variety of reward mechanisms. The most common motivation, and the one that yields the fastes...
Breast Cancer is one of the most common causes of cancer death in women, representing a very complex disease with varied molecular alterations. To assist breast cancer prognosis, the classification of patients into biological groups is of great significance for treatment strategies. Recent studies have used an ensemble of multiple clustering algori...
In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncer...
Public Goods Games (PGGs) are a standard experimental economic approach to studying cooperative behaviour. There are two types of games: discrete-time and continuous-time PGGs. While discrete-time PGGs (one-shot decisions about contributions to public goods) can be easily done as lab experiments, continuous-time PGGs (where participants can change...
The premise of this working paper is based around agent-based simulation models and how to go about creating them from given incomplete information. Agent-based simulations are stochastic simulations that revolve around groups of agents that each have their own characteristics and can make decisions. Such simulations can be used to emulate real lif...
Fuzzy sets may have complex, non-normal or non-convex membership functions that occur, for example, in the output of a fuzzy logic system or when automatically generating fuzzy sets from data. Measuring the distance between such non-standard fuzzy sets can be challenging as there is no clear correct method of comparison and limited research current...
In recent years, researchers have become increasingly more interested in designing an interpretable Fuzzy Logic System (FLS). Many studies have claimed that reducing the complexity of FLSs can lead to improved model interpretability. That is, reducing the number of rules tends to reduce the complexity of FLSs, thus improving their interpretability....
Although driving behaviour has been largely studied amongst private motor vehicles drivers, the literature addressing heavy goods vehicle (HGV) drivers is scarce. Identifying the existing groups of driving stereotypes and their proportions enables researchers, companies and policy makers to establish group-specific strategies to improve safety and...
Sentiment analysis aims to uncover emotions conveyed through information. In its simplest form, it is performed on a polarity basis, where the goal is to classify information with positive or negative emotion. Recent research has explored more nuanced ways to perform emotion analysis. Unsupervised emotion analysis methods require a critical resourc...
Real world environments face a wide range of sources of noise and uncertainty. Thus, the ability to handle various uncertainties, including noise, becomes an indispensable element of automated decision making. Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to tackle uncertainty within the design of fuzzy systems. The firing strength...
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...
Similarity measures are useful for reasoning about fuzzy sets. Hence, many classical set-theoretic similarity measures have been extended for comparing fuzzy sets. In previous work, a set-theoretic similarity measure considering the bidirectional subsethood for intervals was introduced. The measure addressed specific concerns of many common similar...