Special Issue on Genetic Fuzzy Systems and the Interpretability–Accuracy Trade-off

This special issue encompasses four papers devoted to the recent developments in the field of ‘‘Genetic fuzzy systems and the trade-off between interpretability and accuracy’’. The issue was originated from several contributions presented at the First International Workshop on Genetic Fuzzy Systems (GFS2005) that was held in Granada, Spain, March 17–19, 2005. Six conference papers were selected and the authors were asked to develop extended versions which were submitted to the special issue. Each of them was revised by at least three referees and finally four of them were accepted according to the reviewers’ evaluations

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

Modeling and Optimal Design of Machining-Induced Residual Stresses in Aluminium Alloys Using a Fast Hierarchical Multiobjective Optimization Algorithm

The residual stresses induced during shaping and machining play an important role in determining the integrity and durability of metal components. An important issue of producing safety critical components is to find the machining parameters that create compressive surface stresses or minimise tensile surface stresses. In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows constructing transparent fuzzy models considering both accuracy and interpretability attributes of fuzzy systems. The new method employs a hierarchical optimisation structure to improve the modelling efficiency, where two learning mechanisms cooperate together: NSGA-II is used to improve the model’s structure while the gradient descent method is used to optimise the numerical parameters. This hybrid approach is then successfully applied to the problem that concerns the prediction of machining induced residual stresses in aerospace aluminium alloys. Based on the developed reliable prediction models, NSGA-II is further applied to the multi-objective optimal design of aluminium alloys in a ‘reverse-engineering’ fashion. It is revealed that the optimal machining regimes to minimise the residual stress and the machining cost simultaneously can be successfully located

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

New Structural Evolving Algorithms For Fuzzy Systems

Recently, the issue of accuracy and interpretability trade-off has been getting more attention when designing new fuzzy systems. In this thesis, three evolving fuzzy models, namely enhancement of fuzzy term identification (EFTI), structure identification method (SIM) and structural evolving approach (SEA) are proposed to spot the best trade-off between accuracy and interpretability. EFTI, SIM and SEA are designed based on error reducing methods. EFTI is developed to fit with single input single output (SISO) problems (i.e. one dimension), while SIM and SEA are developed to fit with multi input single output (MISO) (medium and high dimension). EFTI begins with a simple fuzzy structure that is composed of two fuzzy terms in the input space. Then EFTI continues evolving by identifying splitting points of the input space that are compatible with the consequent parameters. On the other hand, SIM and SEA start with one fuzzy rule that has no fuzzy term in the input space regardless of the degree level of input dimension. Then they evolve on the basis of either closure or split processes for the selected input attribute of the selected subregion. If the selected attribute has no fuzzy terms, closure is performed, otherwise split is done. The evolving continues until a satisfactory accuracy is fulfilled or maximum number of subregion is reached. A partitioning technique based on the similarity feature and a static partition-selection technique are developed for SIM. While, a partitioning technique based on splitting the selected subregion into two subregions with maximum and minimum average error and a dynamic partition-selection technique are developed for SEA. Furthermore, a pruning technique based on the importance level of the fuzzy rules is proposed to shrink the rule-base of SEA. Compared with SISO models and using three datasets, EFTI produces the lowest RMSE with lowest number of rules. For MISO models and using nine benchmark datasets, SIM achieves the lowest RMSE with the smallest size of rule-base systems. Similarly, for MISO state-of-the-art models and using six benchmark datasets, SEA also produces the lowest RMSE with the smallest size of rule-base systems. In conclusion, the results proved that EFTI, SIM and SEA are able to produce a significant trade-off between accuracy and interpretabilit

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

A Multi-Agent Architecture for the Design of Hierarchical Interval Type-2 Beta Fuzzy System

This paper presents a new methodology for building and evolving hierarchical fuzzy systems. For the system design, a tree-based encoding method is adopted to hierarchically link low dimensional fuzzy systems. Such tree structural representation has by nature a flexible design offering more adjustable and modifiable structures. The proposed hierarchical structure employs a type-2 beta fuzzy system to cope with the faced uncertainties, and the resulting system is called the Hierarchical Interval Type-2 Beta Fuzzy System (HT2BFS). For the system optimization, two main tasks of structure learning and parameter tuning are applied. The structure learning phase aims to evolve and learn the structures of a population of HT2BFS in a multiobjective context taking into account the optimization of both the accuracy and the interpretability metrics. The parameter tuning phase is applied to refine and adjust the parameters of the system. To accomplish these two tasks in the most optimal and faster way, we further employ a multi-agent architecture to provide both a distributed and a cooperative management of the optimization tasks. Agents are divided into two different types based on their functions: a structure agent and a parameter agent. The main function of the structure agent is to perform a multi-objective evolutionary structure learning step by means of the Multi-Objective Immune Programming algorithm (MOIP). The parameter agents have the function of managing different hierarchical structures simultaneously to refine their parameters by means of the Hybrid Harmony Search algorithm (HHS). In this architecture, agents use cooperation and communication concepts to create high-performance HT2BFSs. The performance of the proposed system is evaluated by several comparisons with various state of art approaches on noise-free and noisy time series prediction data sets and regression problems. The results clearly demonstrate a great improvement in the accuracy rate, the convergence speed and the number of used rules as compared with other existing approaches