An artificial immune systems based predictive modelling approach for the multi-objective elicitation of Mamdani fuzzy rules: a special application to modelling alloys

In this paper, a systematic multi-objective Mamdani fuzzy modeling approach is proposed, which can be viewed as an extended version of the previously proposed Singleton fuzzy modeling paradigm. A set of new back-error propagation (BEP) updating formulas are derived so that they can replace the old set developed in the singleton version. With the substitution, the extension to the multi-objective Mamdani Fuzzy Rule-Based Systems (FRBS) is almost endemic. Due to the carefully chosen output membership functions, the inference and the defuzzification methods, a closed form integral can be deducted for the defuzzification method, which ensures the efficiency of the developed Mamdani FRBS. Some important factors, such as the variable length coding scheme and the rule alignment, are also discussed. Experimental results for a real data set from the steel industry suggest that the proposed approach is capable of eliciting not only accurate but also transparent FRBS with good generalization ability

On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

A Robust Multilabel Method Integrating Rule-based Transparent Model, Soft Label Correlation Learning and Label Noise Resistance

Model transparency, label correlation learning and the robust-ness to label noise are crucial for multilabel learning. However, few existing methods study these three characteristics simultaneously. To address this challenge, we propose the robust multilabel Takagi-Sugeno-Kang fuzzy system (R-MLTSK-FS) with three mechanisms. First, we design a soft label learning mechanism to reduce the effect of label noise by explicitly measuring the interactions between labels, which is also the basis of the other two mechanisms. Second, the rule-based TSK FS is used as the base model to efficiently model the inference relationship be-tween features and soft labels in a more transparent way than many existing multilabel models. Third, to further improve the performance of multilabel learning, we build a correlation enhancement learning mechanism based on the soft label space and the fuzzy feature space. Extensive experiments are conducted to demonstrate the superiority of the proposed method.Comment: This paper has been accepted by IEEE Transactions on Fuzzy System

Evolutionary Fuzzy Systems for Explainable Artificial Intelligence: Why, When, What for, and Where to?

Evolutionary fuzzy systems are one of the greatest advances within the area of computational intelligence. They consist of evolutionary algorithms applied to the design of fuzzy systems. Thanks to this hybridization, superb abilities are provided to fuzzy modeling in many different data science scenarios. This contribution is intended to comprise a position paper developing a comprehensive analysis of the evolutionary fuzzy systems research field. To this end, the "4 W" questions are posed and addressed with the aim of understanding the current context of this topic and its significance. Specifically, it will be pointed out why evolutionary fuzzy systems are important from an explainable point of view, when they began, what they are used for, and where the attention of researchers should be directed to in the near future in this area. They must play an important role for the emerging area of eXplainable Artificial Intelligence (XAI) learning from data

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

On-Line Construction and Rule Base Simplification by Replacement in Fuzzy Systems Applied to a Wastewater Treatment Plant

Evolving Takagi-Sugeno (eTS) fuzzy models are used to build a computational model for the WasteWater Treatment Plant (WWTP) in a paper mill. The fuzzy rule base is constructed on-line from data using a recursive fuzzy clustering algorithm that develops the model structure and parameters. In order to avoid some redundancy in the fuzzy rule base mechanisms for merging membership functions and simplifying fuzzy rules are introduced. The rule base simplification is done by replacement allowing the preservation of the rule (cluster) centres as data points belonging to the original data set. Results for the WWTP show that it is possible to build less complex models and preserve a good balance between accuracy and transparency. Copyright © 2005 IFA

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