Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

Improved uncertainty capture for nonsingleton fuzzy systems

In non-singleton fuzzy logic systems (NSFLSs), input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both: the appropriate modelling in the input fuzzy sets of the uncertainties present in the system’s inputs, and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and thus affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed, and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input’s uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time series predictions, where the NSFLSs’ inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared to the standard approach

Changes under the hood - a new type of non-singleton fuzzy logic system

A major asset of fuzzy logic systems is dealing with uncertainties arising in their various applications, thus it is important to make them achieve this task as effectively and comprehensively as possible. While singleton fuzzy logic systems provide some capacity to deal with such uncertainty aspects, non-singleton fuzzy logic systems (NSFLSs) have further enhanced this capacity, particularly in handling input uncertainties. This paper proposes a novel approach to NSFLSs, which further develops this potential by changing the method of handling input fuzzy sets within the inference engine. While the standard approach is getting the maximum of the intersection between input’s and antecedent’s fuzzy sets (in the ”pre-filtering” stage), it is proposed to employ the centroid of the intersection as the basis of each rule’s firing degree. The motivation is to capture the interaction of input and antecedent fuzzy sets with high fidelity, thus making NSFLSs more sensitive to the input’s uncertainty information. The testbed is the common problem of Mackey-Glass time series prediction in the presence of input noise. Analyses of the results show that the new method outperforms the standard approach (by reducing the prediction error) and has potential for a more efficient uncertainty handling in NSFLS applications

Contrasting singleton type-1 and interval type-2 non-singleton type-1 fuzzy logic systems

Most applications of both type-1 and type-2 fuzzy logic systems are employing singleton fuzzification due to its simplicity and reduction in its computational speed. However, using singleton fuzzification assumes that the input data (i.e., measurements) are precise with no uncertainty associated with them. This paper explores the potential of combining the uncertainty modelling capacity of interval type-2 fuzzy sets with the simplicity of type-1 fuzzy logic systems (FLSs) by using interval type-2 fuzzy sets solely as part of the non-singleton input fuzzifier. This paper builds on previous work and uses the methodological design of the footprint of uncertainty (FOU) of interval type-2 fuzzy sets for given levels of uncertainty. We provide a detailed investigation into the ability of both types of fuzzy sets (type-1 and interval type-2) to capture and model different levels of uncertainty/noise through varying the size of the FOU of the underlying input fuzzy sets from type-1 fuzzy sets to very “wide” interval type-2 fuzzy sets as part of type-1 non-singleton FLSs using interval type-2 input fuzzy sets. By applying the study in the context of chaotic time-series prediction, we show how, as uncertainty/noise increases, interval type-2 input fuzzy sets with FOUs of increasing size become more and more viable

Exploring subsethood to determine firing strength in non-singleton fuzzy logic systems

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 has a significant role in the accuracy of FLSs, being based on the interaction of the input and antecedent fuzzy sets. Recent studies have shown that the standard technique for determining firing strengths risks substantial information loss in terms of the interaction of the input and antecedents. Recently, this issue has been addressed through exploration of alternative approaches which employ the centroid of the intersection (cen-NS) and the similarity (sim-NS) between input and antecedent fuzzy sets. This paper identifies potential shortcomings in respect to the previously introduced similarity-based NSFLSs in which firing strength is defined as the similarity between an input FS and an antecedent. To address these shortcomings, this paper explores the potential of the subsethood measure to generate a more suitable firing level (sub-NS) in NSFLSs featuring various noise levels. In the experiment, the basic waiter tipping fuzzy logic system is used to examine the behaviour of sub-NS in comparison with the current approaches. Analysis of the results shows that the sub-NS approach can lead to more stable behaviour in real world applications

ADONiS - Adaptive Online Non-Singleton Fuzzy Logic Systems

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 variations in the level of input-affecting noise, common in real-world applications. The method removes the requirement for both a priori knowledge of noise levels or relying on offline training procedures to define input FS parameters. To the best of our knowledge, the proposed ADaptive, ONline Non-Singleton (ADONiS) Fuzzy Logic System (FLS) framework represents the first end-to-end framework to adaptively configure non-singleton input FSs. The latter is achieved through online uncertainty detection applied to a sliding window of observations. Since real-world environments are influenced by a broad range of noise sources, which can vary greatly in magnitude over time, the proposed technique for combining online determination of noise levels with associated adaptation of input FSs provides an efficient and effective solution which elegantly models input uncertainty in the FLS's input FSs, without requiring changes in any other part (e.g. antecedents, rules or consequents) of the FLS. In this paper, two common chaotic time series (Mackey-Glass, Lorenz) are used to perform prediction experiments to demonstrate and evaluate the proposed framework. Results indicate that the proposed adaptive NSFLS framework provides significant advantages, particularly in environments that include high variation in noise levels, which are common in real-world applications

Noise parameter estimation for non-singleton fuzzy logic systems

Real-world environments face a wide range of noise (uncertainty) sources and gaining insight into the level of noise is a critical part of many applications. While Non-Singleton Fuzzy Logic Systems (NSFLSs), in particular recently introduced advanced variants such as centroid-based NSFLSs have the capacity to handle known quantities of uncertainty, thus far, the actual level of uncertainty has had to be defined a priori - i.e. prior to run time of a system or controller. This paper does not focus on such advances within the architecture of NSFLSs, but focuses on a novel two-stage approach for uncertainty handling in fuzzy logic systems which integrates: (i) estimation of noise levels and (ii) the appropriate handling of the noise based on this estimate, by means of a dynamically configured NSFLS. As initial evaluation of the approach, two chaotic nonlinear time series (Mackey-Glass and Lorenz), as well as a real-world Darwin sea level pressure series prediction fuzzy logic systems are implemented and compared to commonly used procedures. The results indicate that the proposed strategy of integrating uncertainty/noise estimation with the capacity of non-singleton fuzzy logic systems has the potential to deliver performance benefits in real-world applications without requiring a priori information on noise levels and thus delivers a first step towards smart, noise-adaptive non-singleton fuzzy logic systems and controllers

Modelo fuzzy genético para a estimação de forças em correntes a partir da medição das frequências naturais

Orientador: Milton Dias JuniorDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: As instalações em alto mar possuem linhas de ancoragem, chamadas de amarras, para proporcionar estabilidade, suporte e sustentação às estruturas. Essas linhas de ancoragem são geralmente compostas por cabos, correntes e cordas de fibra sintética. Quando a solicitação de carga é alta, as linhas de ancoragem devem ser constituídas por corrente. O monitoramento da força atuando nestas correntes é vital para a confiabilidade e segurança da produção de energia. Os métodos atuais para supervisionar as cargas nas amarras são caros e têm muitas incertezas envolvidas. Nesse contexto, propõe-se uma nova metodologia para a estimativa de força em correntes através da medição de suas frequências naturais. Um sistema de inferência difuso e otimizado por um algoritmo genético foi desenvolvido para estimar da carga nas correntes. As entradas dos modelos difusos são as frequências naturais das correntes e a saída é a força estimada. As metodologias Mamdani e Sugeno foram implementadas e comparadas. Funções de pertinência triangular e gaussiana foram usadas para modelar as entradas e a saída. As regras foram definidas de acordo com as relações entre as frequências naturais e a força na corrente. Para otimizar o sistema, o algoritmo genético pode usar como dados de treinamento os resultados fornecidos por um modelo matemático ou por um conjunto de medições. O modelo matemático desenvolvido apresenta boa concordância com os dados experimentais. O modelo genético difuso foi simulado e testado, fornecendo boa precisão na estimativa da força. Finalmente, demonstrou-se que a fuzzificação não singleton pode ser uma ferramenta útil quando as entradas são ruidosasAbstract: Offshore facilities have mooring lines to provide stability, support and holding to the structures. These mooring lines are commonly made up of synthetic fiber ropes, cables and chains. When the load solicitation is high, the mooring lines must be made up of chain. The monitoring of the strength of these chains is vital for the reliability and security of the production of energy. The current methods for supervising the loads on the chains are expensive and have many uncertainties involved. In this context, it is proposed a new methodology for the force estimation in chains through the measurements of their natural frequencies. The present dissertation arises as an improvement of this approach. A fuzzy inference system optimized by a genetic algorithm is introduced to enhance the estimation of the load on the chains. The inputs of the fuzzy models are the natural frequencies of the chains and the output is the estimated force. The Mamdani and Sugeno methodologies were implemented and compared. Triangular and Gaussian membership functions were used to model the inputs and the output. The rules were set according to the relations between the natural frequencies and the force on the chain. To optimize the system, the genetic algorithm can use the results provided by a mathematical model or by a set of measurements as training data. The mathematical model has good agreement with the experimental data. The fuzzy genetic model was simulated and tested providing good accuracy in estimating the force. In addition, the non-singleton fuzzification demonstrated that can be a helpful tool when the entries are noisyMestradoMecanica de Solidos e Projeto MecanicoMestre em Engenharia Mecânica33003017CAPE

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

Real-world utility of non-singleton fuzzy logic systems: a case of environmental management

The potentials of non-singleton fuzzy logic systems (NSFLSs) in dealing with uncertainties are widely known. However, their utilities and possible challenges in real-world applications, particularly beyond fuzzy controls, are still not widely examined. This paper presents some user-centric design approaches in making NSFLSs usable in a real-world problem of environmental management. In previous work, a singleton FLS was developed based on an established environmental management framework. After further investigation of the users’ requirements, it was realized that the effective capture, representation and visualization of the system’s inputs and outputs are critical, particularly when there are uncertainties involved in data collection and decision-making processes. For addressing the new requirements, the system has been extended to a NSFLS, so it can make use of non-singleton fuzzification in handling uncertain (e.g., noisy) environmental data. Inspired by the user-centric design of this particular system extension, the contribution of this paper is the development of some practical methods to capture/represent input/output uncertainties in NSFLSs. Subject to further users evaluation, the explained methods have potential to be employed in many similar real-world applications, thus extending the NSFLSs applicability to a wider context than the present