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

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

Multi-objective evolutionary–fuzzy augmented flight control for an F16 aircraft

In this article, the multi-objective design of a fuzzy logic augmented flight controller for a high performance fighter jet (the Lockheed-Martin F16) is described. A fuzzy logic controller is designed and its membership functions tuned by genetic algorithms in order to design a roll, pitch, and yaw flight controller with enhanced manoeuverability which still retains safety critical operation when combined with a standard inner-loop stabilizing controller. The controller is assessed in terms of pilot effort and thus reduction of pilot fatigue. The controller is incorporated into a six degree of freedom motion base real-time flight simulator, and flight tested by a qualified pilot instructor

Temporal fuzzy association rule mining with 2-tuple linguistic representation

This paper reports on an approach that contributes towards the problem of discovering fuzzy association rules that exhibit a temporal pattern. The novel application of the 2-tuple linguistic representation identifies fuzzy association rules in a temporal context, whilst maintaining the interpretability of linguistic terms. Iterative Rule Learning (IRL) with a Genetic Algorithm (GA) simultaneously induces rules and tunes the membership functions. The discovered rules were compared with those from a traditional method of discovering fuzzy association rules and results demonstrate how the traditional method can loose information because rules occur at the intersection of membership function boundaries. New information can be mined from the proposed approach by improving upon rules discovered with the traditional method and by discovering new rules

Improving Transparency in Approximate Fuzzy Modeling Using Multi-objective Immune-Inspired Optimisation

In this paper, an immune inspired multi-objective fuzzy modeling (IMOFM) mechanism is proposed specifically for high-dimensional regression problems. For such problems, prediction accuracy is often the paramount requirement. With such a requirement in mind, however, one should also put considerable efforts in eliciting models which are as transparent as possible, a ‘tricky’ exercise in itself. The proposed mechanism adopts a multi-stage modeling procedure and a variable length coding scheme to account for the enlarged search space due to simultaneous optimisation of the rule-base structure and its associated parameters. We claim here that IMOFM can account for both Singleton and Mamdani Fuzzy Rule-Based Systems (FRBS) due to the carefully chosen output membership functions, the inference scheme and the defuzzification method. The proposed modeling approach has been compared to other representatives using a benchmark problem, and was further applied to a high-dimensional problem, taken from the steel industry, which concerns the prediction of mechanical properties of hot rolled steels. Results confirm that IMOFM is capable of eliciting not only accurate but also transparent FRBSs from quantitative data

A new fuzzy set merging technique using inclusion-based fuzzy clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

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

Self learning neuro-fuzzy modeling using hybrid genetic probabilistic approach for engine air/fuel ratio prediction

Machine Learning is concerned in constructing models which can learn and make predictions based on data. Rule extraction from real world data that are usually tainted with noise, ambiguity, and uncertainty, automatically requires feature selection. Neuro-Fuzzy system (NFS) which is known with its prediction performance has the difficulty in determining the proper number of rules and the number of membership functions for each rule. An enhanced hybrid Genetic Algorithm based Fuzzy Bayesian classifier (GA-FBC) was proposed to help the NFS in the rule extraction. Feature selection was performed in the rule level overcoming the problems of the FBC which depends on the frequency of the features leading to ignore the patterns of small classes. As dealing with a real world problem such as the Air/Fuel Ratio (AFR) prediction, a multi-objective problem is adopted. The GA-FBC uses mutual information entropy, which considers the relevance between feature attributes and class attributes. A fitness function is proposed to deal with multi-objective problem without weight using a new composition method. The model was compared to other learning algorithms for NFS such as Fuzzy c-means (FCM) and grid partition algorithm. Predictive accuracy and the complexity of the Fuzzy Rule Base System (FRBS) including number of rules and number of terms in each rule were taken as terms of evaluation. It was also compared to the original GA-FBC depending on the frequency not on Mutual Information (MI). Experimental results using Air/Fuel Ratio (AFR) data sets show that the new model participates in decreasing the average number of attributes in the rule and sometimes in increasing the average performance compared to other models. This work facilitates in achieving a self-generating FRBS from real data. The GA-FBC can be used as a new direction in machine learning research. This research contributes in controlling automobile emissions in helping the reduction of one of the most causes of pollution to produce greener environment