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

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

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

Model fusion using fuzzy aggregation: Special applications to metal properties

To improve the modelling performance, one should either propose a new modelling methodology or make the best of existing models. In this paper, the study is concentrated on the latter solution, where a structure-free modelling paradigm is proposed. It does not rely on a fixed structure and can combine various modelling techniques in ‘symbiosis’ using a ‘master fuzzy system’. This approach is shown to be able to include the advantages of different modelling techniques altogether by requiring less training and by minimising the efforts relating optimisation of the final structure. The proposed approach is then successfully applied to the industrial problems of predicting machining induced residual stresses for aerospace alloy components as well as modelling the mechanical properties of heat-treated alloy steels, both representing complex, non-linear and multi-dimensional environments

Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms

AbstractThe identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this paper a multi-objective evolutionary approach is proposed to determine a Pareto-optimum set of fuzzy systems with different compromises between their accuracy and complexity. In particular, two fundamental and competing objectives concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained system. Another key aspect of the algorithm presented in this work is the use of some new expert evolutionary operators, specifically designed for the problem of fuzzy function approximation, that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm

Interpretable fuzzy modeling using multi-objective immune-inspired optimization algorithms

Abstract—In this paper, an immune inspired multi-objective fuzzy modeling (IMOFM) mechanism is proposed specifically for high-dimensional regression problems. For such problems, high predictive accuracy is often the paramount requirement. With such a requirement in mind, however, one should also put considerable efforts in making the elicited model as interpretable as possible, which leads to a difficult optimization problem. The proposed modeling approach adopts a multi-stage modeling procedure and a variable length coding scheme to account for the enlarged search space due to the simultaneous optimization of the rule-base structure and its associated parameters. IMOFM can account for both Singleton and Mamdani Fuzzy Rule-Based Systems (FRBS) due to the carefully chosen output membership functions, the inference and the defuzzification methods. The proposed algorithm has been compared with other representatives using a simple benchmark problem, and has also been applied to a high-dimensional problem which models mechanical properties of hot rolled steels. Results confirm that IMOFM can elicit accurate and yet transparent FRBSs from quantitative data

An Artificial Immune Systems based Predictive Modelling Approach for the Multi-Objective Elicitation of Mamdani Fuzzy Rules A Special Application to Modelling Alloys

Abstract-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

Data Mining in Smart Grids

Effective smart grid operation requires rapid decisions in a data-rich, but information-limited, environment. In this context, grid sensor data-streaming cannot provide the system operators with the necessary information to act on in the time frames necessary to minimize the impact of the disturbances. Even if there are fast models that can convert the data into information, the smart grid operator must deal with the challenge of not having a full understanding of the context of the information, and, therefore, the information content cannot be used with any high degree of confidence. To address this issue, data mining has been recognized as the most promising enabling technology for improving decision-making processes, providing the right information at the right moment to the right decision-maker. This Special Issue is focused on emerging methodologies for data mining in smart grids. In this area, it addresses many relevant topics, ranging from methods for uncertainty management, to advanced dispatching. This Special Issue not only focuses on methodological breakthroughs and roadmaps in implementing the methodology, but also presents the much-needed sharing of the best practices. Topics include, but are not limited to, the following: Fuzziness in smart grids computing Emerging techniques for renewable energy forecasting Robust and proactive solution of optimal smart grids operation Fuzzy-based smart grids monitoring and control frameworks Granular computing for uncertainty management in smart grids Self-organizing and decentralized paradigms for information processin