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

An immune algorithm based fuzzy predictive modeling mechanism using variable length coding and multi-objective optimization allied to engineering materials processing

In this paper, a systematic multi-objective fuzzy modeling approach is proposed, which can be regarded as a three-stage modeling procedure. In the first stage, an evolutionary based clustering algorithm is developed to extract an initial fuzzy rule base from the data. Based on this model, a back-propagation algorithm with momentum terms is used to refine the initial fuzzy model. The refined model is then used to seed the initial population of an immune inspired multi-objective optimization algorithm in the third stage to obtain a set of fuzzy models with improved transparency. To tackle the problem of simultaneously optimizing the structure and parameters, a variable length coding scheme is adopted to improve the efficiency of the search. The proposed modeling approach is applied to a real data set from the steel industry. Results show that the proposed approach is capable of eliciting not only accurate but also transparent fuzzy models

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 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

Classification of Explainable Artificial Intelligence Methods through Their Output Formats

Machine and deep learning have proven their utility to generate data-driven models with high accuracy and precision. However, their non-linear, complex structures are often difficult to interpret. Consequently, many scholars have developed a plethora of methods to explain their functioning and the logic of their inferences. This systematic review aimed to organise these methods into a hierarchical classification system that builds upon and extends existing taxonomies by adding a significant dimension—the output formats. The reviewed scientific papers were retrieved by conducting an initial search on Google Scholar with the keywords “explainable artificial intelligence”; “explainable machine learning”; and “interpretable machine learning”. A subsequent iterative search was carried out by checking the bibliography of these articles. The addition of the dimension of the explanation format makes the proposed classification system a practical tool for scholars, supporting them to select the most suitable type of explanation format for the problem at hand. Given the wide variety of challenges faced by researchers, the existing XAI methods provide several solutions to meet the requirements that differ considerably between the users, problems and application fields of artificial intelligence (AI). The task of identifying the most appropriate explanation can be daunting, thus the need for a classification system that helps with the selection of methods. This work concludes by critically identifying the limitations of the formats of explanations and by providing recommendations and possible future research directions on how to build a more generally applicable XAI method. Future work should be flexible enough to meet the many requirements posed by the widespread use of AI in several fields, and the new regulation

A Survey of Neural Trees

Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to integrate NNs and DTs explicitly or implicitly. In this survey, these approaches are organized in a school which we term as neural trees (NTs). This survey aims to present a comprehensive review of NTs and attempts to identify how they enhance the model interpretability. We first propose a thorough taxonomy of NTs that expresses the gradual integration and co-evolution of NNs and DTs. Afterward, we analyze NTs in terms of their interpretability and performance, and suggest possible solutions to the remaining challenges. Finally, this survey concludes with a discussion about other considerations like conditional computation and promising directions towards this field. A list of papers reviewed in this survey, along with their corresponding codes, is available at: https://github.com/zju-vipa/awesome-neural-treesComment: 35 pages, 7 figures and 1 tabl