Christian Wagner

Dani Kiyasseh, Runzhuo Ma, Taseen F. Haque et al.

Surgery is a high-stakes domain where surgeons must navigate critical anatomical structures and actively avoid potential complications while achieving the main task at hand. Such surgical activity has been shown to affect long-term patient outcomes. To better understand this relationship, whose mechanics remain unknown for the majority of surgical procedures, we hypothesize that the core elements of surgery must first be quantified in a reliable, objective, and scalable manner. We believe this is a prerequisite for the provision of surgical feedback and modulation of surgeon performance in pursuit of improved patient outcomes. To holistically quantify surgeries, we propose a unified deep learning framework, entitled Roboformer, which operates exclusively on videos recorded during surgery to independently achieve multiple tasks: surgical phase recognition (the what of surgery), gesture classification and skills assessment (the how of surgery). We validated our framework on four video-based datasets of two commonly-encountered types of steps (dissection and suturing) within minimally-invasive robotic surgeries. We demonstrated that our framework can generalize well to unseen videos, surgeons, medical centres, and surgical procedures. We also found that our framework, which naturally lends itself to explainable findings, identified relevant information when achieving a particular task. These findings are likely to instill surgeons with more confidence in our framework's behaviour, increasing the likelihood of clinical adoption, and thus paving the way for more targeted surgical feedback.

Direnc Pekaslan, Jose Maria Alonso-Moral, Kasun Bandara et al.

This paper presents the real-world smart-meter dataset and offers an analysis of solutions derived from the Energy Prediction Technical Challenges, focusing primarily on two key competitions: the IEEE Computational Intelligence Society (IEEE-CIS) Technical Challenge on Energy Prediction from Smart Meter data in 2020 (named EP) and its follow-up challenge at the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) in 2021 (named as XEP). These competitions focus on accurate energy consumption forecasting and the importance of interpretability in understanding the underlying factors. The challenge aims to predict monthly and yearly estimated consumption for households, addressing the accurate billing problem with limited historical smart meter data. The dataset comprises 3,248 smart meters, with varying data availability ranging from a minimum of one month to a year. This paper delves into the challenges, solutions and analysing issues related to the provided real-world smart meter data, developing accurate predictions at the household level, and introducing evaluation criteria for assessing interpretability. Additionally, this paper discusses aspects beyond the competitions: opportunities for energy disaggregation and pattern detection applications at the household level, significance of communicating energy-driven factors for optimised billing, and emphasising the importance of responsible AI and data privacy considerations. These aspects provide insights into the broader implications and potential advancements in energy consumption prediction. Overall, these competitions provide a dataset for residential energy research and serve as a catalyst for exploring accurate forecasting, enhancing interpretability, and driving progress towards the discussion of various aspects such as energy disaggregation, demand response programs or behavioural interventions.

Stephen B. Broomell, Christian Wagner

Information aggregation is a vital tool for human and machine decision making in the presence of uncertainty. Traditionally, approaches to aggregation broadly diverge into two categories, those which attribute a worth or weight to information sources and those which attribute said worth to the evidence arising from said sources. The latter is pervasive in the physical sciences, underpinning linear order statistics and enabling non-linear aggregation. The former is popular in the social sciences, providing interpretable insight on the sources. While prior work has identified the need to apply both approaches simultaneously, it has yet to conceptually integrate both approaches and provide a semantic interpretation of the arising aggregation approach. Here, we conceptually integrate both approaches in a novel joint weighted averaging operator. We leverage compositional geometry to underpin this integration, showing how it provides a systematic basis for the combination of weighted aggregation operators--which has thus far not been considered in the literature. We proceed to show how the resulting operator systematically integrates a priori beliefs about the worth of both sources and evidence, reflecting the semantic integration of both weighting strategies. We conclude and highlight the potential of the operator across disciplines, from machine learning to psychology.

Michael DelRose, Christian Wagner, Philip Frederick

The ability to predict the intentions of people based solely on their visual actions is a skill only performed by humans and animals. The intelligence of current computer algorithms has not reached this level of complexity, but there are several research efforts that are working towards it. With the number of classification algorithms available, it is hard to determine which algorithm works best for a particular situation. In classification of visual human intent data, Hidden Markov Models (HMM), and their variants, are leading candidates. The inability of HMMs to provide a probability in the observation to observation linkages is a big downfall in this classification technique. If a person is visually identifying an action of another person, they monitor patterns in the observations. By estimating the next observation, people have the ability to summarize the actions, and thus determine, with pretty good accuracy, the intention of the person performing the action. These visual cues and linkages are important in creating intelligent algorithms for determining human actions based on visual observations. The Evidence Feed Forward Hidden Markov Model is a newly developed algorithm which provides observation to observation linkages. The following research addresses the theory behind Evidence Feed Forward HMMs, provides mathematical proofs of their learning of these parameters to optimize the likelihood of observations with a Evidence Feed Forwards HMM, which is important in all computational intelligence algorithm, and gives comparative examples with standard HMMs in classification of both visual action data and measurement data; thus providing a strong base for Evidence Feed Forward HMMs in classification of many types of problems.

Ruizhe Li, Grazziela Figueredo, Dorothee Auer et al.

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 methods excel at global alignment, they often perform worse in aligning local regions. To address this challenge, this paper proposes a mask-guided encoder-decoder DCNN-based image registration method, named as MrRegNet. This approach employs a multi-resolution encoder for feature extraction and subsequently estimates multi-resolution displacement fields in the decoder to handle the substantial deformation of images. Furthermore, segmentation masks are employed to direct the model's attention toward aligning local regions. The results show that the proposed method outperforms traditional methods like Demons and a well-known deep learning method, VoxelMorph, on a public 3D brain MRI dataset (OASIS) and a local 2D brain MRI dataset with large deformations. Importantly, the image alignment accuracies are significantly improved at local regions guided by segmentation masks. Github link:https://github.com/ruizhe-l/MrRegNet.

Xi Li, Nicholas Matsumoto, Ujjwal Pasupulety et al.

Fine-grained analysis of intraoperative behavior and its impact on patient outcomes remain a longstanding challenge. We present Frame-to-Outcome (F2O), an end-to-end system that translates tissue dissection videos into gesture sequences and uncovers patterns associated with postoperative outcomes. Leveraging transformer-based spatial and temporal modeling and frame-wise classification, F2O robustly detects consecutive short (~2 seconds) gestures in the nerve-sparing step of robot-assisted radical prostatectomy (AUC: 0.80 frame-level; 0.81 video-level). F2O-derived features (gesture frequency, duration, and transitions) predicted postoperative outcomes with accuracy comparable to human annotations (0.79 vs. 0.75; overlapping 95% CI). Across 25 shared features, effect size directions were concordant with small differences (~ 0.07), and strong correlation (r = 0.96, p < 1e-14). F2O also captured key patterns linked to erectile function recovery, including prolonged tissue peeling and reduced energy use. By enabling automatic interpretable assessment, F2O establishes a foundation for data-driven surgical feedback and prospective clinical decision support.

Ruizhe Li, Matteo Bastiani, Dorothee Auer et al.

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 analysis tasks, including brain age estimation. However, the performance and generalisability of the deep learning model are highly dependent on the quantity and quality of the training data set. Both collecting and annotating brain MRI data are extremely time-consuming. In this paper, to overcome the data scarcity problem, we propose a generative adversarial network (GAN) based image synthesis method. Different from the existing GAN-based methods, we integrate a task-guided branch (a regression model for age estimation) to the end of the generator in GAN. By adding a task-guided loss to the conventional GAN loss, the learned low-dimensional latent space and the synthesised images are more task-specific. It helps to boost the performance of the down-stream task by combining the synthesised images and real images for model training. The proposed method was evaluated on a public brain MRI data set for age estimation. Our proposed method outperformed (statistically significant) a deep convolutional neural network based regression model and the GAN-based image synthesis method without the task-guided branch. More importantly, it enables the identification of age-related brain regions in the image space. The code is available on GitHub (https://github.com/ruizhe-l/tgb-gan).

Zack Ellerby, Christian Wagner, Stephen Broomell

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 point values - but sometimes a range of options may better represent the correct answer. In this paper, we propose an efficient interval-valued response mode, whereby responses are made by marking an ellipse along a continuous scale. We discuss its potential to capture and quantify valuable information that would be lost using conventional approaches, while preserving a high degree of response-efficiency. The information captured by the response interval may represent a possible response range - i.e., a conjunctive set, such as the real numbers between three and six. Alternatively, it may reflect uncertainty in respect to a distinct response - i.e., a disjunctive set, such as a confidence interval. We then report a validation study, utilizing our recently introduced open-source software (DECSYS) to explore how interval-valued survey responses reflect experimental manipulations of several factors hypothesised to influence interval width, across multiple contexts. Results consistently indicate that respondents used interval widths effectively, and subjective participant feedback was also positive. We present this as initial empirical evidence for the efficacy and value of interval-valued response capture. Interestingly, our results also provide insight into respondents' reasoning about the different aforementioned types of intervals - we replicate a tendency towards overconfidence for those representing epistemic uncertainty (i.e., disjunctive sets), but find intervals representing inherent range (i.e., conjunctive sets) to be well-calibrated.

Chao Chen, Christian Wagner, Jonathan M. Garibaldi

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 design from a machine learning perspective. In other words, while representations such as neural networks have benefited from a boom in learning capability driven by an increase in computational performance in combination with advances in their training mechanisms and available tool, in particular gradient descent, the impact on fuzzy system design has been limited. In this paper, we discuss gradient-descent-based optimisation of fuzzy systems, focussing in particular on automatic differentiation -- crucial to neural network learning -- with a view to free fuzzy system designers from intricate derivative computations, allowing for more focus on the functional and explainability aspects of their design. As a starting point, we present a use case in FuzzyR which demonstrates how current fuzzy inference system implementations can be adjusted to leverage powerful features of automatic differentiation tools sets, discussing its potential for the future of fuzzy system design.

Shreyank N Gowda, Xiaobo Jin, Christian Wagner

In cross-modal retrieval tasks, such as image-to-report and report-to-image retrieval, accurately aligning medical images with relevant text reports is essential but challenging due to the inherent ambiguity and variability in medical data. Existing models often struggle to capture the nuanced, multi-level semantic relationships in radiology data, leading to unreliable retrieval results. To address these issues, we propose the Prototype-Enhanced Confidence Modeling (PECM) framework, which introduces multi-level prototypes for each modality to better capture semantic variability and enhance retrieval robustness. PECM employs a dual-stream confidence estimation that leverages prototype similarity distributions and an adaptive weighting mechanism to control the impact of high-uncertainty data on retrieval rankings. Applied to radiology image-report datasets, our method achieves significant improvements in retrieval precision and consistency, effectively handling data ambiguity and advancing reliability in complex clinical scenarios. We report results on multiple different datasets and tasks including fully supervised and zero-shot retrieval obtaining performance gains of up to 10.17%, establishing in new state-of-the-art.

Shaily Kabir, Christian Wagner, Zack Ellerby

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, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward -- offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for insight. Following recent progress in the capture of interval-valued data, including from human participants, conducting machine learning directly upon intervals is a crucial next step. This paper focuses on linear regression for interval-valued data as a recent growth area, providing an essential foundation for broader use of intervals in AI. We conduct an in-depth analysis of state-of-the-art methods, elucidating their behaviour, advantages, and pitfalls when applied to datasets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence -- i.e., ensuring that models maintain fundamental mathematical properties of intervals throughout -- and the paper puts forward extensions to an existing approach to guarantee this. Carefully designed experiments, using both synthetic and real-world data, are conducted -- with findings presented alongside novel visualizations for interval-valued regression outputs, designed to maximise model interpretability. Finally, the paper makes recommendations concerning method suitability for data sets with specific properties and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source.

Ruizhe Li, Dorothee Auer, Christian Wagner et al.

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 address this problem, we propose a generic semi-supervised learning framework for image segmentation based on a deep convolutional neural network (DCNN). An encoder-decoder based DCNN is initially trained using a few annotated training samples. This initially trained model is then copied into sub-models and improved iteratively using random subsets of unlabeled data with pseudo labels generated from models trained in the previous iteration. The number of sub-models is gradually decreased to one in the final iteration. We evaluate the proposed method on a public grand-challenge dataset for skin lesion segmentation. Our method is able to significantly improve beyond fully supervised model learning by incorporating unlabeled data.

Philipp Leinen, Malte Esders, Kristof T. Schütt et al.

The ability to handle single molecules as effectively as macroscopic building-blocks would enable the construction of complex supramolecular structures inaccessible to self-assembly. The fundamental challenges obstructing this goal are the uncontrolled variability and poor observability of atomic-scale conformations. Here, we present a strategy to work around both obstacles, and demonstrate autonomous robotic nanofabrication by manipulating single molecules. Our approach employs reinforcement learning (RL), which finds solution strategies even in the face of large uncertainty and sparse feedback. We demonstrate the potential of our RL approach by removing molecules autonomously with a scanning probe microscope from a supramolecular structure -- an exemplary task of subtractive manufacturing at the nanoscale. Our RL agent reaches an excellent performance, enabling us to automate a task which previously had to be performed by a human. We anticipate that our work opens the way towards autonomous agents for the robotic construction of functional supramolecular structures with speed, precision and perseverance beyond our current capabilities.

Zack Ellerby, Josie McCulloch, Melanie Wilson et al.

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 information is useful for determining attack risk, but much of it is challenging to acquire automatically and instead must be collected through expert assessments. However, most experts inherently carry some degree of uncertainty in their assessments. For example, it is impossible to be certain precisely how many tools are available to aid an attack. Traditional methods of capturing subjective judgements through choices such as \emph{high}, \emph{medium} or \emph{low} do not enable experts to quantify their uncertainty. However, it is important to measure the range of uncertainty surrounding responses in order to appropriately inform system vulnerability analysis. We use a recently introduced interval-valued response-format to capture uncertainty in experts' judgements and employ inferential statistical approaches to analyse the data. We identify key attributes that contribute to hop vulnerability in cyber-systems and demonstrate the value of capturing the uncertainty around these attributes. We find that this uncertainty is not only predictive of uncertainty in the overall vulnerability of a given system component, but also significantly informs ratings of overall component vulnerability itself. We propose that these methods and associated insights can be employed in real world situations, including vulnerability assessments of cyber-physical systems, which are becoming increasingly complex and integrated into society, making them particularly susceptible to uncertainty in assessment.

Javier Navarro, Christian Wagner

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., Type-1, Interval Type-2, General Type-2). Arguably, one of the most flexible techniques is the Interval Agreement Approach (IAA) as it allows to model the perception of all respondents without making assumptions such as outlier removal or predefined membership function types (e.g. Gaussian). A key aspect in the analysis of interval-valued data and indeed, IAA based agreement models of said data, is to determine the position and strengths of agreement across all the sources/participants. While previously, the Agreement Ratio was proposed to measure the strength of agreement in fuzzy set based models of interval data, said measure has only been applicable to type-1 fuzzy sets. In this paper, we extend the Agreement Ratio to capture the degree of inter-group agreement modelled by a General Type-2 Fuzzy Set when using the IAA. This measure relies on using a similarity measure to quantitatively express the relation between the different levels of agreement in a given FS. Synthetic examples are provided in order to demonstrate both behaviour and calculation of the measure. Finally, an application to real-world data is provided in order to show the potential of this measure to assess the divergence of opinions for ambiguous concepts when heterogeneous groups of participants are involved.

Polla Fattah, Uwe Aickelin, Christian Wagner

An important issue in public goods game is whether player's behaviour changes over time, and if so, how significant it is. In this game players can be classified into different groups according to the level of their participation in the public good. This problem can be considered as a concept drift problem by asking the amount of change that happens to the clusters of players over a sequence of game rounds. In this study we present a method for measuring changes in clusters with the same items over discrete time points using external clustering validation indices and area under the curve. External clustering indices were originally used to measure the difference between suggested clusters in terms of clustering algorithms and ground truth labels for items provided by experts. Instead of different cluster label comparison, we use these indices to compare between clusters of any two consecutive time points or between the first time point and the remaining time points to measure the difference between clusters through time points. In theory, any external clustering indices can be used to measure changes for any traditional (non-temporal) clustering algorithm, due to the fact that any time point alone is not carrying any temporal information. For the public goods game, our results indicate that the players are changing over time but the change is smooth and relatively constant between any two time points.

Simon Miller, Christian Wagner, Uwe Aickelin et al.

An important role carried out by cyber-security experts is the assessment of proposed computer systems, during their design stage. This task is fraught with difficulties and uncertainty, making the knowledge provided by human experts essential for successful assessment. Today, the increasing number of progressively complex systems has led to an urgent need to produce tools that support the expert-led process of system-security assessment. In this research, we use weighted averages (WAs) and ordered weighted averages (OWAs) with evolutionary algorithms (EAs) to create aggregation operators that model parts of the assessment process. We show how individual overall ratings for security components can be produced from ratings of their characteristics, and how these individual overall ratings can be aggregated to produce overall rankings of potential attacks on a system. As well as the identification of salient attacks and weak points in a prospective system, the proposed method also highlights which factors and security components contribute most to a component's difficulty and attack ranking respectively. A real world scenario is used in which experts were asked to rank a set of technical attacks, and to answer a series of questions about the security components that are the subject of the attacks. The work shows how finding good aggregation operators, and identifying important components and factors of a cyber-security problem can be automated. The resulting operators have the potential for use as decision aids for systems designers and cyber-security experts, increasing the amount of assessment that can be achieved with the limited resources available.

Javier Navarro, Christian Wagner, Uwe Aickelin et al.

In the context of cancer treatment and surgery, quality of life assessment is a crucial part of determining treatment success and viability. In order to assess it, patients completed questionnaires which employ words to capture aspects of patients well-being are the norm. As the results of these questionnaires are often used to assess patient progress and to determine future treatment options, it is important to establish that the words used are interpreted in the same way by both patients and medical professionals. In this paper, we capture and model patients perceptions and associated uncertainty about the words used to describe the level of their physical function used in the highly common (in Sarcoma Services) Toronto Extremity Salvage Score (TESS) questionnaire. The paper provides detail about the interval-valued data capture as well as the subsequent modelling of the data using fuzzy sets. Based on an initial sample of participants, we use Jaccard similarity on the resulting words models to show that there may be considerable differences in the interpretation of commonly used questionnaire terms, thus presenting a very real risk of miscommunication between patients and medical professionals as well as within the group of medical professionals.

Javier Navarro, Christian Wagner, Uwe Aickelin

Fuzzy Rule-Based Classification Systems (FRBCSs) have the potential to provide so-called interpretable classifiers, i.e. classifiers which can be introspective, understood, validated and augmented by human experts by relying on fuzzy-set based rules. This paper builds on prior work for interval type-2 fuzzy set based FRBCs where the fuzzy sets and rules of the classifier are generated using an initial clustering stage. By introducing Subtractive Clustering in order to identify multiple cluster prototypes, the proposed approach has the potential to deliver improved classification performance while maintaining good interpretability, i.e. without resulting in an excessive number of rules. The paper provides a detailed overview of the proposed FRBC framework, followed by a series of exploratory experiments on both linearly and non-linearly separable datasets, comparing results to existing rule-based and SVM approaches. Overall, initial results indicate that the approach enables comparable classification performance to non rule-based classifiers such as SVM, while often achieving this with a very small number of rules.

Polla Fattah, Uwe Aickelin, Christian Wagner

This study optimises manually derived rule-based expert system classification of objects according to changes in their properties over time. One of the key challenges that this study tries to address is how to classify objects that exhibit changes in their behaviour over time, for example how to classify companies' share price stability over a period of time or how to classify students' preferences for subjects while they are progressing through school. A specific case the paper considers is the strategy of players in public goods games (as common in economics) across multiple consecutive games. Initial classification starts from expert definitions specifying class allocation for players based on aggregated attributes of the temporal data. Based on these initial classifications, the optimisation process tries to find an improved classifier which produces the best possible compact classes of objects (players) for every time point in the temporal data. The compactness of the classes is measured by a cost function based on internal cluster indices like the Dunn Index, distance measures like Euclidean distance or statistically derived measures like standard deviation. The paper discusses the approach in the context of incorporating changing player strategies in the aforementioned public good games, where common classification approaches so far do not consider such changes in behaviour resulting from learning or in-game experience. By using the proposed process for classifying temporal data and the actual players' contribution during the games, we aim to produce a more refined classification which in turn may inform the interpretation of public goods game data.

Grazziela P. Figueredo, Christian Wagner, Jonathan M. Garibaldi et al.

In this position paper, we present ideas about creating a next generation framework towards an adaptive interface for data communication and visualisation systems. Our objective is to develop a system that accepts large data sets as inputs and provides user-centric, meaningful visual information to assist owners to make sense of their data collection. The proposed framework comprises four stages: (i) the knowledge base compilation, where we search and collect existing state-ofthe-art visualisation techniques per domain and user preferences; (ii) the development of the learning and inference system, where we apply artificial intelligence techniques to learn, predict and recommend new graphic interpretations (iii) results evaluation; and (iv) reinforcement and adaptation, where valid outputs are stored in our knowledge base and the system is iteratively tuned to address new demands. These stages, as well as our overall vision, limitations and possible challenges are introduced in this article. We also discuss further extensions of this framework for other knowledge discovery tasks.

Josie McCulloch, Christian Wagner, Uwe Aickelin

Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs of fuzzy sets. This is particularly a problem where many fuzzy sets are generated from real data, and while two different measures may be used to automatically compare such fuzzy sets, it is difficult to interpret two different results. This is especially true where a large number of fuzzy sets are being compared as part of a reasoning system. This paper introduces a method for combining the results of multiple measures into a single measure for the purpose of analysing and comparing fuzzy sets. The combined measure alleviates ambiguous results and aids in the automatic comparison of fuzzy sets. The properties of the combined measure are given, and demonstrations are presented with discussions on the advantages over using a single measure.

Josie C. McCullochy, Chris J. Hinde, Christian Wagner et al.

The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory, however, distance measures currently within the literature use a crisp value to represent the distance between fuzzy sets. A real valued distance measure is developed into a fuzzy distance measure which better reflects the uncertainty inherent in fuzzy sets and a fuzzy directional distance measure is presented, which accounts for the direction of change between fuzzy sets. A multiplicative version is explored as a full maximal assignment is computationally intractable so an intermediate solution is offered.

Josie McCulloch, Christian Wagner, Uwe Aickelin

The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets.

Josie McCulloch, Christian Wagner, Uwe Aickelin

Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.

Ian Dent, Christian Wagner, Uwe Aickelin et al.

Changes in the UK electricity market mean that domestic users will be required to modify their usage behaviour in order that supplies can be maintained. Clustering allows usage profiles collected at the household level to be clustered into groups and assigned a stereotypical profile which can be used to target marketing campaigns. Fuzzy C Means clustering extends this by allowing each household to be a member of many groups and hence provides the opportunity to make personalised offers to the household dependent on their degree of membership of each group. In addition, feedback can be provided on how user's changing behaviour is moving them towards more "green" or cost effective stereotypical usage.