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

Fuzzy Adaptive Tuning of a Particle Swarm Optimization Algorithm for Variable-Strength Combinatorial Test Suite Generation

Combinatorial interaction testing is an important software testing technique that has seen lots of recent interest. It can reduce the number of test cases needed by considering interactions between combinations of input parameters. Empirical evidence shows that it effectively detects faults, in particular, for highly configurable software systems. In real-world software testing, the input variables may vary in how strongly they interact, variable strength combinatorial interaction testing (VS-CIT) can exploit this for higher effectiveness. The generation of variable strength test suites is a non-deterministic polynomial-time (NP) hard computational problem \cite{BestounKamalFuzzy2017}. Research has shown that stochastic population-based algorithms such as particle swarm optimization (PSO) can be efficient compared to alternatives for VS-CIT problems. Nevertheless, they require detailed control for the exploitation and exploration trade-off to avoid premature convergence (i.e. being trapped in local optima) as well as to enhance the solution diversity. Here, we present a new variant of PSO based on Mamdani fuzzy inference system \cite{Camastra2015,TSAKIRIDIS2017257,KHOSRAVANIAN2016280}, to permit adaptive selection of its global and local search operations. We detail the design of this combined algorithm and evaluate it through experiments on multiple synthetic and benchmark problems. We conclude that fuzzy adaptive selection of global and local search operations is, at least, feasible as it performs only second-best to a discrete variant of PSO, called DPSO. Concerning obtaining the best mean test suite size, the fuzzy adaptation even outperforms DPSO occasionally. We discuss the reasons behind this performance and outline relevant areas of future work.Comment: 21 page

Optimization of Evolutionary Neural Networks Using Hybrid Learning Algorithms

Evolutionary artificial neural networks (EANNs) refer to a special class of artificial neural networks (ANNs) in which evolution is another fundamental form of adaptation in addition to learning. Evolutionary algorithms are used to adapt the connection weights, network architecture and learning algorithms according to the problem environment. Even though evolutionary algorithms are well known as efficient global search algorithms, very often they miss the best local solutions in the complex solution space. In this paper, we propose a hybrid meta-heuristic learning approach combining evolutionary learning and local search methods (using 1st and 2nd order error information) to improve the learning and faster convergence obtained using a direct evolutionary approach. The proposed technique is tested on three different chaotic time series and the test results are compared with some popular neuro-fuzzy systems and a recently developed cutting angle method of global optimization. Empirical results reveal that the proposed technique is efficient in spite of the computational complexity

Knowledge discovery for friction stir welding via data driven approaches: Part 2 – multiobjective modelling using fuzzy rule based systems

In this final part of this extensive study, a new systematic data-driven fuzzy modelling approach has been developed, taking into account both the modelling accuracy and its interpretability (transparency) as attributes. For the first time, a data-driven modelling framework has been proposed designed and implemented in order to model the intricate FSW behaviours relating to AA5083 aluminium alloy, consisting of the grain size, mechanical properties, as well as internal process properties. As a result, ‘Pareto-optimal’ predictive models have been successfully elicited which, through validations on real data for the aluminium alloy AA5083, have been shown to be accurate, transparent and generic despite the conservative number of data points used for model training and testing. Compared with analytically based methods, the proposed data-driven modelling approach provides a more effective way to construct prediction models for FSW when there is an apparent lack of fundamental process knowledge

Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework

AbstractIn this paper we propose a multi-objective evolutionary algorithm to generate Mamdani fuzzy rule-based systems with different good trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we introduce the concepts of virtual and concrete rule bases: the former is defined on linguistic variables, all partitioned with a fixed maximum number of fuzzy sets, while the latter takes into account, for each variable, a number of fuzzy sets as determined by the specific partition granularity of that variable. We exploit a chromosome composed of two parts, which codify the variables partition granularities, and the virtual rule base, respectively. Genetic operators manage virtual rule bases, whereas fitness evaluation relies on an appropriate mapping strategy between virtual and concrete rule bases. The algorithm has been tested on two real-world regression problems showing very promising results

Decision Making in the Medical Domain: Comparing the Effectiveness of GP-Generated Fuzzy Intelligent Structures

ABSTRACT: In this work, we examine the effectiveness of two intelligent models in medical domains. Namely, we apply grammar-guided genetic programming to produce fuzzy intelligent structures, such as fuzzy rule-based systems and fuzzy Petri nets, in medical data mining tasks. First, we use two context-free grammars to describe fuzzy rule-based systems and fuzzy Petri nets with genetic programming. Then, we apply cellular encoding in order to express the fuzzy Petri nets with arbitrary size and topology. The models are examined thoroughly in four real-world medical data sets. Results are presented in detail and the competitive advantages and drawbacks of the selected methodologies are discussed, in respect to the nature of each application domain. Conclusions are drawn on the effectiveness and efficiency of the presented approach

Automatic synthesis of fuzzy systems: An evolutionary overview with a genetic programming perspective

Studies in Evolutionary Fuzzy Systems (EFSs) began in the 90s and have experienced a fast development since then, with applications to areas such as pattern recognition, curve‐fitting and regression, forecasting and control. An EFS results from the combination of a Fuzzy Inference System (FIS) with an Evolutionary Algorithm (EA). This relationship can be established for multiple purposes: fine‐tuning of FIS's parameters, selection of fuzzy rules, learning a rule base or membership functions from scratch, and so forth. Each facet of this relationship creates a strand in the literature, as membership function fine‐tuning, fuzzy rule‐based learning, and so forth and the purpose here is to outline some of what has been done in each aspect. Special focus is given to Genetic Programming‐based EFSs by providing a taxonomy of the main architectures available, as well as by pointing out the gaps that still prevail in the literature. The concluding remarks address some further topics of current research and trends, such as interpretability analysis, multiobjective optimization, and synthesis of a FIS through Evolving methods

Literature Review of the Recent Trends and Applications in various Fuzzy Rule based systems

Fuzzy rule based systems (FRBSs) is a rule-based system which uses linguistic fuzzy variables as antecedents and consequent to represent human understandable knowledge. They have been applied to various applications and areas throughout the soft computing literature. However, FRBSs suffers from many drawbacks such as uncertainty representation, high number of rules, interpretability loss, high computational time for learning etc. To overcome these issues with FRBSs, there exists many extensions of FRBSs. This paper presents an overview and literature review of recent trends on various types and prominent areas of fuzzy systems (FRBSs) namely genetic fuzzy system (GFS), hierarchical fuzzy system (HFS), neuro fuzzy system (NFS), evolving fuzzy system (eFS), FRBSs for big data, FRBSs for imbalanced data, interpretability in FRBSs and FRBSs which use cluster centroids as fuzzy rules. The review is for years 2010-2021. This paper also highlights important contributions, publication statistics and current trends in the field. The paper also addresses several open research areas which need further attention from the FRBSs research community.Comment: 49 pages, Accepted for publication in ijf

Evolutionary Learning of Fuzzy Rules for Regression

The objective of this PhD Thesis is to design Genetic Fuzzy Systems (GFS) that learn Fuzzy Rule Based Systems to solve regression problems in a general manner. Particularly, the aim is to obtain models with low complexity while maintaining high precision without using expert-knowledge about the problem to be solved. This means that the GFSs have to work with raw data, that is, without any preprocessing that help the learning process to solve a particular problem. This is of particular interest, when no knowledge about the input data is available or for a first approximation to the problem. Moreover, within this objective, GFSs have to cope with large scale problems, thus the algorithms have to scale with the data