Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

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.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

Employing zSlices based general type-2 fuzzy sets to model multi level agreement

In this paper, we introduce the concept of Multi Level Agreement (MLA) based on (zSlices based) general type-2 fuzzy sets. We define the notion of MLA and describe how it can be computed based on a series of interval type-2 fuzzy sets. We provide examples, visualizing the nature of MLA sets and discuss their properties and interpretation. Moreover, we specifically address the reason for introducing MLA in order to allow the modeling of agreement in real world applications using fuzzy sets while still maintaining an uncertainty model and show that the use of general type-2 fuzzy sets is essential for MLA as classical sets, type-1 and interval type-2 fuzzy sets do not provide a degree of freedom which could be employed to model agreement. © 2011 IEEE

Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets

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

Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets

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

Type-2 Fuzzy Logic based Systems for Adaptive Learning and Teaching within Intelligent E-Learning Environments

The recent years have witnessed an increased interest in e-learning platforms that incorporate adaptive learning and teaching systems that enable the creation of adaptive learning environments to suit individual student needs. The efficiency of these adaptive educational systems relies on the methodology used to accurately gather and examine information pertaining to the characteristics and needs of students and relies on the way that information is processed to form an adaptive learning context. The vast majority of existing adaptive educational systems do not learn from the users’ behaviours to create white-box models to handle the high level of uncertainty and that could be easily read and analysed by the lay user. The data generated from interactions, such as teacher–learner or learner–system interactions within asynchronous environments, provide great opportunities to realise more adaptive and intelligent e-learning platforms rather than propose prescribed pedagogy that depends on the idea of a few designers and experts. Another limitation of current adaptive educational systems is that most of the existing systems ignore gauging the students' engagements levels and mapping them to suitable delivery needs which match the students' knowledge and preferred learning styles. It is necessary to estimate the degree of students’ engagement with the course contents. Such feedback is highly important and useful for assessing the teaching quality and adjusting the teaching delivery in small and large-scale online learning platforms. Furthermore, most of the current adaptive educational systems are used within asynchronous e-learning contexts as self-paced e-learning products in which learners can study in their own time and at their own speed, totally ignorant of synchronous e-learning settings of teacher-led delivery of the learning material over a communication tool in real time. This thesis presents novel theoretical and practical architectures based on computationally lightweight T2FLSs for lifelong learning and adaptation of learners’ and teachers’ behaviours in small- and large-scale asynchronous and synchronous e-learning platforms. In small-scale asynchronous and synchronous e-learning platforms, the presented architecture augments an engagement estimate system using a noncontact, low-cost, and multiuser support 3D sensor Kinect (v2). This is able to capture reliable features including head pose direction and hybrid features of facial expression to enable convenient and robust estimation of engagement in small-scale online and onsite learning in an unconstrained and natural environment in which users are allowed to act freely and move without restrictions. We will present unique real-world experiments in large and small-scale e-learning platforms carried out by 1,916 users from King Abdul-Aziz and Essex universities in Saudi Arabia and the UK over the course of teaching Excel and PowerPoint in which the type 2 system is learnt and adapted to student and teacher behaviour. The type-2 fuzzy system will be subjected to extended and varied knowledge, engagement, needs, and a high level of uncertainty variation in e-learning environments outperforming the type 1 fuzzy system and non-adaptive version of the system by producing better performance in terms of improved learning, completion rates, and better user engagements

IMPROVING UNDERSTANDABILITY AND UNCERTAINTY MODELING OF DATA USING FUZZY LOGIC SYSTEMS

The need for automation, optimality and efficiency has made modern day control and monitoring systems extremely complex and data abundant. However, the complexity of the systems and the abundance of raw data has reduced the understandability and interpretability of data which results in a reduced state awareness of the system. Furthermore, different levels of uncertainty introduced by sensors and actuators make interpreting and accurately manipulating systems difficult. Classical mathematical methods lack the capability to capture human knowledge and increase understandability while modeling such uncertainty. Fuzzy Logic has been shown to alleviate both these problems by introducing logic based on vague terms that rely on human understandable terms. The use of linguistic terms and simple consequential rules increase the understandability of system behavior as well as data. Use of vague terms and modeling data from non-discrete prototypes enables modeling of uncertainty. However, due to recent trends, the primary research of fuzzy logic have been diverged from the basic concept of understandability. Furthermore, high computational costs to achieve robust uncertainty modeling have led to restricted use of such fuzzy systems in real-world applications. Thus, the goal of this dissertation is to present algorithms and techniques that improve understandability and uncertainty modeling using Fuzzy Logic Systems. In order to achieve this goal, this dissertation presents the following major contributions: 1) a novel methodology for generating Fuzzy Membership Functions based on understandability, 2) Linguistic Summarization of data using if-then type consequential rules, and 3) novel Shadowed Type-2 Fuzzy Logic Systems for uncertainty modeling. Finally, these presented techniques are applied to real world systems and data to exemplify their relevance and usage

Fuzzy Transfer Learning

The use of machine learning to predict output from data, using a model, is a well studied area. There are, however, a number of real-world applications that require a model to be produced but have little or no data available of the specific environment. These situations are prominent in Intelligent Environments (IEs). The sparsity of the data can be a result of the physical nature of the implementation, such as sensors placed into disaster recovery scenarios, or where the focus of the data acquisition is on very defined user groups, in the case of disabled individuals. Standard machine learning approaches focus on a need for training data to come from the same domain. The restrictions of the physical nature of these environments can severely reduce data acquisition making it extremely costly, or in certain situations, impossible. This impedes the ability of these approaches to model the environments. It is this problem, in the area of IEs, that this thesis is focussed. To address complex and uncertain environments, humans have learnt to use previously acquired information to reason and understand their surroundings. Knowledge from different but related domains can be used to aid the ability to learn. For example, the ability to ride a road bicycle can help when acquiring the more sophisticated skills of mountain biking. This humanistic approach to learning can be used to tackle real-world problems where a-priori labelled training data is either difficult or not possible to gain. The transferral of knowledge from a related, but differing context can allow for the reuse and repurpose of known information. In this thesis, a novel composition of methods are brought together that are broadly based on a humanist approach to learning. Two concepts, Transfer Learning (TL) and Fuzzy Logic (FL) are combined in a framework, Fuzzy Transfer Learning (FuzzyTL), to address the problem of learning tasks that have no prior direct contextual knowledge. Through the use of a FL based learning method, uncertainty that is evident in dynamic environments is represented. By combining labelled data from a contextually related source task, and little or no unlabelled data from a target task, the framework is shown to be able to accomplish predictive tasks using models learned from contextually different data. The framework incorporates an additional novel five stage online adaptation process. By adapting the underlying fuzzy structure through the use of previous labelled knowledge and new unlabelled information, an increase in predictive performance is shown. The framework outlined is applied to two differing real-world IEs to demonstrate its ability to predict in uncertain and dynamic environments. Through a series of experiments, it is shown that the framework is capable of predicting output using differing contextual data

Context-aware intelligent decisions: online assessment of heavy goods vehicle driving risk

There is a growing interest in assessing the impact of drivers' actions and behaviours on road safety due to the numerous road fatalities and costs attributed to them. For Heavy Goods Vehicle (HGV) drivers, assessing the road safety risks of their behaviours is a subject of interest for researchers, governments and transport companies, as nations rely on HGVs for the delivery of goods and services. However, HGV driving is a complex, dynamic, uncertain and multifaceted task, mostly influenced by individual traits and external contextual factors. Advanced computational and artificial intelligence (AI) methods have provided promising solutions to automatically characterise the manner by which drivers operate vehicle controls and assess their impact on road safety. However, several challenges and limitations are faced by the current intelligence-supported driving risk assessment approaches proposed by researchers, such as: (1) the lack of comprehensive driving risk datasets; (2) information about the impact of inevitable contextual factors on HGV drivers' responses is not considered, such as drivers' physical and mental states, weather conditions, traffic conditions, road geometry, road types, and work schedules; (3) ambiguity in the definition of driving behaviours is not considered; and (4) imprecision of AI models, and variability in experts' subjective views are not considered. To overcome the aforementioned challenges and limitations, this multidisciplinary research aims at exploring multiple sources of data including information about the impact of contextual factors captured from crucial stakeholders in the HGV sector to develop a reliable context-aware driving risk assessment framework. To achieve this aim, AI methods are explored to accurately detect drivers' driving styles, affective states and driving postures using telematics data, facial images, and driver posture images respectively. Subsequently, due to the lack of comprehensive driving risk datasets, fuzzy expert systems (FESs) are explored to fuse detected driving behaviours and perceived external factors using knowledge from domain experts. The key findings of this research are: (1) recurrent neural networks are effective in capturing the temporal dynamics and differences between the different types of driver distraction postures and affective states; (2) there is a trade-off between efficiency and privacy in processing facial images using AI approaches; (3) the fusion of driver behaviours and external factors using FESs produces realistic, reliable and fair driving risk assessments; and (4) a hierarchical representation of a decision-making process simplifies reasoning compared to flat representations

Context-aware intelligent decisions: online assessment of heavy goods vehicle driving risk

There is a growing interest in assessing the impact of drivers' actions and behaviours on road safety due to the numerous road fatalities and costs attributed to them. For Heavy Goods Vehicle (HGV) drivers, assessing the road safety risks of their behaviours is a subject of interest for researchers, governments and transport companies, as nations rely on HGVs for the delivery of goods and services. However, HGV driving is a complex, dynamic, uncertain and multifaceted task, mostly influenced by individual traits and external contextual factors. Advanced computational and artificial intelligence (AI) methods have provided promising solutions to automatically characterise the manner by which drivers operate vehicle controls and assess their impact on road safety. However, several challenges and limitations are faced by the current intelligence-supported driving risk assessment approaches proposed by researchers, such as: (1) the lack of comprehensive driving risk datasets; (2) information about the impact of inevitable contextual factors on HGV drivers' responses is not considered, such as drivers' physical and mental states, weather conditions, traffic conditions, road geometry, road types, and work schedules; (3) ambiguity in the definition of driving behaviours is not considered; and (4) imprecision of AI models, and variability in experts' subjective views are not considered. To overcome the aforementioned challenges and limitations, this multidisciplinary research aims at exploring multiple sources of data including information about the impact of contextual factors captured from crucial stakeholders in the HGV sector to develop a reliable context-aware driving risk assessment framework. To achieve this aim, AI methods are explored to accurately detect drivers' driving styles, affective states and driving postures using telematics data, facial images, and driver posture images respectively. Subsequently, due to the lack of comprehensive driving risk datasets, fuzzy expert systems (FESs) are explored to fuse detected driving behaviours and perceived external factors using knowledge from domain experts. The key findings of this research are: (1) recurrent neural networks are effective in capturing the temporal dynamics and differences between the different types of driver distraction postures and affective states; (2) there is a trade-off between efficiency and privacy in processing facial images using AI approaches; (3) the fusion of driver behaviours and external factors using FESs produces realistic, reliable and fair driving risk assessments; and (4) a hierarchical representation of a decision-making process simplifies reasoning compared to flat representations

Towards Better Performance in the Face of Input Uncertainty while Maintaining Interpretability in AI

Uncertainty is a pervasive element of many real-world applications and very often existing sources of uncertainty (e.g. atmospheric conditions, economic parameters or precision of measurement devices) have a detrimental impact on the input and ultimately results of decision-support systems. Thus, the ability to handle input uncertainty is a valuable component of real-world decision-support systems. There is a vast amount of literature on handling of uncertainty through decision-support systems. While they handle uncertainty and deliver a good performance, providing an insight into the decision process (e.g. why or how results are produced) is another important asset in terms of having trust in or providing a ‘debugging’ process in given decisions. Fuzzy set theory provides the basis for Fuzzy Logic Systems which are often associated with the ability for handling uncertainty and possessing mechanisms for providing a degree of interpretability. Specifically, Non-Singleton Fuzzy Logic Systems are essential in dealing with uncertainty that affects input which is one of the main sources of uncertainty in real-world systems. Therefore, in this thesis, we comprehensively explore enhancing non-singleton fuzzy logic systems capabilities considering both capturing-handling uncertainty and also maintaining interpretability. To that end the following three key aspects are investigated; (i) to faithfully map input uncertainty to outputs of systems, (ii) to propose a new framework to provide the ability for dynamically adapting system on-the-fly in changing real-world environments. (iii) to maintain level of interpretability while leveraging performance of systems. The first aspect is to leverage mapping uncertainty from input to outputs of systems through the interaction between input and antecedent fuzzy sets i.e. firing strengths. In the context of Non-Singleton Fuzzy Logic Systems, recent studies have shown that the standard technique for determining firing strengths risks information loss in terms of the interaction of the input uncertainty and antecedent fuzzy sets. This thesis explores and puts forward novel approaches to generating firing strengths which faithfully map the uncertainty affecting system inputs to outputs. Time-series forecasting experiments are used to evaluate the proposed alternative firing strength generating technique under different levels of input uncertainty. The analysis of the results shows that the proposed approach can also be a suitable method to generate appropriate firing levels which provide the ability to map different uncertainty levels from input to output of FLS that are likely to occur in real-world circumstances. The second aspect is to provide dynamic adaptive behaviours to systems at run-time in changing conditions which are common in real-world environments. Traditionally, in the fuzzification step of Non-Singleton Fuzzy Logic Systems, approaches are generally limited to the selection of a single type of input fuzzy sets to capture the input uncertainty, whereas input uncertainty levels tend to be inherently varying over time in the real-world at run-time. Thus, in this thesis, input uncertainty is modelled -where it specifically arises- in an online manner which can provide an adaptive behaviour to capture varying input uncertainty levels. The framework is presented to generate Type-1 or Interval Type-2 input fuzzy sets, called ADaptive Online Non-singleton fuzzy logic System (ADONiS). In the proposed framework, an uncertainty estimation technique is utilised on a sequence of observations to continuously update the input fuzzy sets of non-singleton fuzzy logic systems. Both the type-1 and interval type-2 versions of the ADONiS frameworks remove the limitation of the selection of a specific type of input fuzzy sets. Also this framework enables input fuzzy sets to be adapted to unknown uncertainty levels which is not perceived at the design stage of the model. Time-series forecasting experiments are implemented and results show that our proposed framework provides performance advantages over traditional counterpart approaches, particularly in environments that include high variation in noise levels, which are common in real-world applications. In addition, the real-world medical application study is designed to test the deployability of the ADONiS framework and to provide initial insight in respect to its viability in replacing traditional approaches. The third aspect is to maintain levels of interpretability, while increasing performance of systems. When a decision-support model delivers a good performance, providing an insight of the decision process is also an important asset in terms of trustworthiness, safety and ethical aspects etc. Fuzzy logic systems are considered to possess mechanisms which can provide a degree of interpretability. Traditionally, while optimisation procedures provide performance benefits in fuzzy logic systems, they often cause alterations in components (e.g. rule set, parameters, or fuzzy partitioning structures) which can lead to higher accuracy but commonly do not consider the interpretability of the resulting model. In this thesis, the state of the art in fuzzy logic systems interpretability is advanced by capturing input uncertainty in the fuzzification -where it arises- and by handling it the inference engine step. In doing so, while the performance increase is achieved, the proposed methods limit any optimisation impact to the fuzzification and inference engine steps which protects key components of FLSs (e.g. fuzzy sets, rule parameters etc.) and provide the ability to maintain the given level of interpretability