A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

Multiobjective programming for type-2 hierarchical fuzzy inference trees

This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure. Specifically, a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of HFIT takes place in two phases. Firstly, a nondominated sorting based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (low model’s complexity) with a high accuracy. Secondly, the differential evolution algorithm is applied to optimize the obtained tree’s parameters. In the obtained tree, each node has a different input’s combination, where the evolutionary process governs the input’s combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree’s structural optimization that accept inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by most of the other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selectio

Development of FPGA based Standalone Tunable Fuzzy Logic Controllers

Soft computing techniques differ from conventional (hard) computing, in that unlike hard computing, it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for soft computing is the human mind and its ability to address day-to-day problems. The principal constituents of Soft Computing (SC) are Fuzzy Logic (FL), Evolutionary Computation (EC), Machine Learning (ML) and Artificial Neural Networks (ANNs). This thesis presents a generic hardware architecture for type-I and type-II standalone tunable Fuzzy Logic Controllers (FLCs) in Field Programmable Gate Array (FPGA). The designed FLC system can be remotely configured or tuned according to expert operated knowledge and deployed in different applications to replace traditional Proportional Integral Derivative (PID) controllers. This re-configurability is added as a feature to existing FLCs in literature. The FLC parameters which are needed for tuning purpose are mainly input range, output range, number of inputs, number of outputs, the parameters of the membership functions like slope and center points, and an If-Else rule base for the fuzzy inference process. Online tuning enables users to change these FLC parameters in real-time and eliminate repeated hardware programming whenever there is a need to change. Realization of these systems in real-time is difficult as the computational complexity increases exponentially with an increase in the number of inputs. Hence, the challenge lies in reducing the rule base significantly such that the inference time and the throughput time is perceivable for real-time applications. To achieve these objectives, Modified Rule Active 2 Overlap Membership Function (MRA2-OMF), Modified Rule Active 3 Overlap Membership Function (MRA3-OMF), Modified Rule Active 4 Overlap Membership Function (MRA4-OMF), and Genetic Algorithm (GA) base rule optimization methods are proposed and implemented. These methods reduce the effective rules without compromising system accuracy and improve the cycle time in terms of Fuzzy Logic Inferences Per Second (FLIPS). In the proposed system architecture, the FLC is segmented into three independent modules, fuzzifier, inference engine with rule base, and defuzzifier. Fuzzy systems employ fuzzifier to convert the real world crisp input into the fuzzy output. In type 2 fuzzy systems there are two fuzzifications happen simultaneously from upper and lower membership functions (UMF and LMF) with subtractions and divisions. Non-restoring, very high radix, and newton raphson approximation are most widely used division algorithms in hardware implementations. However, these prevalent methods have a cost of more latency. In order to overcome this problem, a successive approximation division algorithm based type 2 fuzzifier is introduced. It has been observed that successive approximation based fuzzifier computation is faster than the other type 2 fuzzifier. A hardware-software co-design is established on Virtex 5 LX110T FPGA board. The MATLAB Graphical User Interface (GUI) acquires the fuzzy (type 1 or type 2) parameters from users and a Universal Asynchronous Receiver/Transmitter (UART) is dedicated to data communication between the hardware and the fuzzy toolbox. This GUI is provided to initiate control, input, rule transfer, and then to observe the crisp output on the computer. A proposed method which can support canonical fuzzy IF-THEN rules, which includes special cases of the fuzzy rule base is included in Digital Fuzzy Logic Controller (DFLC) architecture. For this purpose, a mealy state machine is incorporated into the design. The proposed FLCs are implemented on Xilinx Virtex-5 LX110T. DFLC peripheral integration with Micro-Blaze (MB) processor through Processor Logic Bus (PLB) is established for Intellectual Property (IP) core validation. The performance of the proposed systems are compared to Fuzzy Toolbox of MATLAB. Analysis of these designs is carried out by using Hardware-In-Loop (HIL) test to control various plant models in MATLAB/Simulink environments

An introduction to DSmT

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout this presentation to show the efficiency and the generality of this new approach

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

Switching control systems and their design automation via genetic algorithms

The objective of this work is to provide a simple and effective nonlinear controller. Our strategy involves switching the underlying strategies in order to maintain a robust control. If a disturbance moves the system outside the region of stability or the domain of attraction, it will be guided back onto the desired course by the application of a different control strategy. In the context of switching control, the common types of controller present in the literature are based either on fuzzy logic or sliding mode. Both of them are easy to implement and provide efficient control for non-linear systems, their actions being based on the observed input/output behaviour of the system. In the field of fuzzy logic control (FLC) using error feedback variables there are two main problems. The first is the poor transient response (jerking) encountered by the conventional 2-dimensional rule-base fuzzy PI controller. Secondly, conventional 3-D rule-base fuzzy PID control design is both computationally intensive and suffers from prolonged design times caused by a large dimensional rule-base. The size of the rule base will increase exponentially with the increase of the number of fuzzy sets used for each input decision variable. Hence, a reduced rule-base is needed for the 3-term fuzzy controller. In this thesis a direct implementation method is developed that allows the size of the rule-base to be reduced exponentially without losing the features of the PID structure. This direct implementation method, when applied to the reduced rule-base fuzzy PI controller, gives a good transient response with no jerking

Heuristic design of fuzzy inference systems: a review of three decades of research

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi–Sugeno–Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper offers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems