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

HYEI: A New Hybrid Evolutionary Imperialist Competitive Algorithm for Fuzzy Knowledge Discovery

In recent years, imperialist competitive algorithm (ICA), genetic algorithm (GA), and hybrid fuzzy classification systems have been successfully and effectively employed for classification tasks of data mining. Due to overcoming the gaps related to ineffectiveness of current algorithms for analysing high-dimension independent datasets, a new hybrid approach, named HYEI, is presented to discover generic rule-based systems in this paper. This proposed approach consists of three stages and combines an evolutionary-based fuzzy system with two ICA procedures to generate high-quality fuzzy-classification rules. Initially, the best feature subset is selected by using the embedded ICA feature selection, and then these features are used to generate basic fuzzy-classification rules. Finally, all rules are optimized by using an ICA algorithm to reduce their length or to eliminate some of them. The performance of HYEI has been evaluated by using several benchmark datasets from the UCI machine learning repository. The classification accuracy attained by the proposed algorithm has the highest classification accuracy in 6 out of the 7 dataset problems and is comparative to the classification accuracy of the 5 other test problems, as compared to the best results previously published

Analysing the Moodle e-learning platform through subgroup discovery algorithms based on evolutionary fuzzy systems

Nowadays, there is a increasing in the use of learning management systems from the universities. This type of systems are also known under other di erent terms as course management systems or learning content management systems. Speci cally, these systems are e-learning platforms o ering di erent facilities for information sharing and communication between the participants in the e-learning process. This contribution presents an experimental study with several subgroup discovery algorithms based on evolutionary fuzzy systems using data from a web-based education system. The main objective of this contribution is to extract unusual subgroups to describe possible relationships between the use of the e-learning platform and marks obtained by the students. The results obtained by the best performing algorithm, NMEEF-SD, are also presented. The most representative results obtained by this algorithm are summarised in order to obtain knowledge that can allow teachers to take actions to improve student performance

Subgroup Discovery trhough Evolutionary Fuzzy Systems applied to Bioinformatic problems

Subgroup discovery is a descriptive data mining technique using supervised learning. This paper presents a summary about the main properties and elements about subgroup discovery task. In addition, we will focus on the suitability and potential of the search performed by evolutionary algorithms in order to apply in the development of subgroup discovery algorithms, and in the use of fuzzy logic which is a soft computing technique very close to the human reasoning. The hybridisation of both techniques are well known as evolutionary fuzzy system. The most relevant applications of evolutionary fuzzy systems for subgroup discovery in the bioinformatics domains are outlined in this work. Specifically, these algorithms are applied to a problem based on the Influenza A virus and the accute sore throat problem

Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms

AbstractThis paper presents a hybrid method for identification of Pareto-optimal fuzzy classifiers (FCs). In contrast to many existing methods, the initial population for multiobjective evolutionary algorithms (MOEAs) is neither created randomly nor a priori knowledge is required. Instead, it is created by the proposed two-step initialization method. First, a decision tree (DT) created by C4.5 algorithm is transformed into an FC. Therefore, relevant variables are selected and initial partition of input space is performed. Then, the rest of the population is created by randomly replacing some parameters of the initial FC, such that, the initial population is widely spread. That improves the convergence of MOEAs into the correct Pareto front. The initial population is optimized by NSGA-II algorithm and a set of Pareto-optimal FCs representing the trade-off between accuracy and interpretability is obtained. The method does not require any a priori knowledge of the number of fuzzy sets, distribution of fuzzy sets or the number of relevant variables. They are all determined by it. Performance of the obtained FCs is validated by six benchmark data sets from the literature. The obtained results are compared to a recently published paper [H. Ishibuchi, Y. Nojima, Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning, International Journal of Approximate Reasoning 44 (1) (2007) 4–31] and the benefits of our method are clearly shown

Subgroup Discovery: Real-World Applications

Subgroup discovery is a data mining technique which extracts interesting rules with respect to a target variable. An important characteristic of this task is the combination of predictive and descriptive induction. In this paper, an overview about subgroup discovery is performed. In addition, di erent real-world applications solved through evolutionary algorithms where the suitability and potential of this type of algorithms for the development of subgroup discovery algorithms are presented

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

Multiobjective Evolutionary Optimization of Type-2 Fuzzy Rule-Based Systems for Financial Data Classification

Classification techniques are becoming essential in the financial world for reducing risks and possible disasters. Managers are interested in not only high accuracy, but in interpretability and transparency as well. It is widely accepted now that the comprehension of how inputs and outputs are related to each other is crucial for taking operative and strategic decisions. Furthermore, inputs are often affected by contextual factors and characterized by a high level of uncertainty. In addition, financial data are usually highly skewed toward the majority class. With the aim of achieving high accuracies, preserving the interpretability, and managing uncertain and unbalanced data, this paper presents a novel method to deal with financial data classification by adopting type-2 fuzzy rule-based classifiers (FRBCs) generated from data by a multiobjective evolutionary algorithm (MOEA). The classifiers employ an approach, denoted as scaled dominance, for defining rule weights in such a way to help minority classes to be correctly classified. In particular, we have extended PAES-RCS, an MOEA-based approach to learn concurrently the rule and data bases of FRBCs, for managing both interval type-2 fuzzy sets and unbalanced datasets. To the best of our knowledge, this is the first work that generates type-2 FRBCs by concurrently maximizing accuracy and minimizing the number of rules and the rule length with the objective of producing interpretable models of real-world skewed and incomplete financial datasets. The rule bases are generated by exploiting a rule and condition selection (RCS) approach, which selects a reduced number of rules from a heuristically generated rule base and a reduced number of conditions for each selected rule during the evolutionary process. The weight associated with each rule is scaled by the scaled dominance approach on the fuzzy frequency of the output class, in order to give a higher weight to the minority class. As regards the data base learning, the membership function parameters of the interval type-2 fuzzy sets used in the rules are learned concurrently to the application of RCS. Unbalanced datasets are managed by using, in addition to complexity, selectivity and specificity as objectives of the MOEA rather than only the classification rate. We tested our approach, named IT2-PAES-RCS, on 11 financial datasets and compared our results with the ones obtained by the original PAES-RCS with three objectives and with and without scaled dominance, the FRBCs, fuzzy association rule-based classification model for high-dimensional dataset (FARC-HD) and fuzzy unordered rules induction algorithm (FURIA), the classical C4.5 decision tree algorithm, and its cost-sensitive version. Using nonparametric statistical tests, we will show that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable with and complexity lower than the ones generated by the two versions of the original PAES-RCS. Further, the FRBCs generated by FARC-HD and FURIA and the decision trees computed by C4.5 and its cost-sensitive version, despite the highest complexity, result to be less accurate than the FRBCs generated by IT2-PAES-RCS. Finally, we will highlight how these FRBCs are easily interpretable by showing and discussing one of them

A fuzzy logic expert system for selecting optimal and sustainable life cycle maintenance and rehabilitation strategies for road pavements

Aged road pavements and insufficient maintenance budgets, along with increasing concerns over the environmental issues related to transportation have introduced additional challenges to highway agencies. Multiobjective optimisation techniques can be used to account for those multiple aspects in the design of maintenance and rehabilitation (M&amp;R) strategies. Contrary to the singleobjective optimisation problems where a single solution is optimal, the solution of multiobjective optimisation problems is a set of non-dominated solutions, often referred to as Pareto-optimal set. This set of optimal solutions represents the trade-off between the different and often conflicting objectives, and in many cases is comprised by a vast number of elements. This paper presents the development and application of a fuzzy logic expert system for selecting a single solution from the Pareto set obtained from the multiobjective optimisation of sustainable pavement M&amp;R strategies. It provides decision-makers with an easy and intuitive methodology for the selection of the most preferred solution according to sustainability criteria. The proposed system is applied to a case study from France. Posteriorly, different strategies reflecting the decision-maker’s preferences towards economic and environmental objectives are analysed. Conclusions and recommendations for future improvements are derived from this application.</p