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

Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling

This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined. First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria. Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions. The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information

Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling

This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined. First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria. Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions. The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information

Decision Support Systems

Decision support systems (DSS) have evolved over the past four decades from theoretical concepts into real world computerized applications. DSS architecture contains three key components: knowledge base, computerized model, and user interface. DSS simulate cognitive decision-making functions of humans based on artificial intelligence methodologies (including expert systems, data mining, machine learning, connectionism, logistical reasoning, etc.) in order to perform decision support functions. The applications of DSS cover many domains, ranging from aviation monitoring, transportation safety, clinical diagnosis, weather forecast, business management to internet search strategy. By combining knowledge bases with inference rules, DSS are able to provide suggestions to end users to improve decisions and outcomes. This book is written as a textbook so that it can be used in formal courses examining decision support systems. It may be used by both undergraduate and graduate students from diverse computer-related fields. It will also be of value to established professionals as a text for self-study or for reference

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios