A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretability of a Neuro-Fuzzy Controller

In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binary-real Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The  approach  is  tested  on  two  control examples:  a single  input  single  output (SISO) system  and  a  multivariable (MIMO) system

Literature Review of the Recent Trends and Applications in various Fuzzy Rule based systems

Fuzzy rule based systems (FRBSs) is a rule-based system which uses linguistic fuzzy variables as antecedents and consequent to represent human understandable knowledge. They have been applied to various applications and areas throughout the soft computing literature. However, FRBSs suffers from many drawbacks such as uncertainty representation, high number of rules, interpretability loss, high computational time for learning etc. To overcome these issues with FRBSs, there exists many extensions of FRBSs. This paper presents an overview and literature review of recent trends on various types and prominent areas of fuzzy systems (FRBSs) namely genetic fuzzy system (GFS), hierarchical fuzzy system (HFS), neuro fuzzy system (NFS), evolving fuzzy system (eFS), FRBSs for big data, FRBSs for imbalanced data, interpretability in FRBSs and FRBSs which use cluster centroids as fuzzy rules. The review is for years 2010-2021. This paper also highlights important contributions, publication statistics and current trends in the field. The paper also addresses several open research areas which need further attention from the FRBSs research community.Comment: 49 pages, Accepted for publication in ijf

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

Evolutionary Computation and QSAR Research

[Abstract] The successful high throughput screening of molecule libraries for a specific biological property is one of the main improvements in drug discovery. The virtual molecular filtering and screening relies greatly on quantitative structure-activity relationship (QSAR) analysis, a mathematical model that correlates the activity of a molecule with molecular descriptors. QSAR models have the potential to reduce the costly failure of drug candidates in advanced (clinical) stages by filtering combinatorial libraries, eliminating candidates with a predicted toxic effect and poor pharmacokinetic profiles, and reducing the number of experiments. To obtain a predictive and reliable QSAR model, scientists use methods from various fields such as molecular modeling, pattern recognition, machine learning or artificial intelligence. QSAR modeling relies on three main steps: molecular structure codification into molecular descriptors, selection of relevant variables in the context of the analyzed activity, and search of the optimal mathematical model that correlates the molecular descriptors with a specific activity. Since a variety of techniques from statistics and artificial intelligence can aid variable selection and model building steps, this review focuses on the evolutionary computation methods supporting these tasks. Thus, this review explains the basic of the genetic algorithms and genetic programming as evolutionary computation approaches, the selection methods for high-dimensional data in QSAR, the methods to build QSAR models, the current evolutionary feature selection methods and applications in QSAR and the future trend on the joint or multi-task feature selection methods.Instituto de Salud Carlos III, PIO52048Instituto de Salud Carlos III, RD07/0067/0005Ministerio de Industria, Comercio y Turismo; TSI-020110-2009-53)Galicia. Consellería de Economía e Industria; 10SIN105004P

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers

Multiobjective Evolutionary Optimization for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs

Multi-Objective Evolutionary Optimisation for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs

Uncertainty and Interpretability Studies in Soft Computing with an Application to Complex Manufacturing Systems

In systems modelling and control theory, the benefits of applying neural networks have been extensively studied. Particularly in manufacturing processes, such as the prediction of mechanical properties of heat treated steels. However, modern industrial processes usually involve large amounts of data and a range of non-linear effects and interactions that might hinder their model interpretation. For example, in steel manufacturing the understanding of complex mechanisms that lead to the mechanical properties which are generated by the heat treatment process is vital. This knowledge is not available via numerical models, therefore an experienced metallurgist estimates the model parameters to obtain the required properties. This human knowledge and perception sometimes can be imprecise leading to a kind of cognitive uncertainty such as vagueness and ambiguity when making decisions. In system classification, this may be translated into a system deficiency - for example, small input changes in system attributes may result in a sudden and inappropriate change for class assignation. In order to address this issue, practitioners and researches have developed systems that are functional equivalent to fuzzy systems and neural networks. Such systems provide a morphology that mimics the human ability of reasoning via the qualitative aspects of fuzzy information rather by its quantitative analysis. Furthermore, these models are able to learn from data sets and to describe the associated interactions and non-linearities in the data. However, in a like-manner to neural networks, a neural fuzzy system may suffer from a lost of interpretability and transparency when making decisions. This is mainly due to the application of adaptive approaches for its parameter identification. Since the RBF-NN can be treated as a fuzzy inference engine, this thesis presents several methodologies that quantify different types of uncertainty and its influence on the model interpretability and transparency of the RBF-NN during its parameter identification. Particularly, three kind of uncertainty sources in relation to the RBF-NN are studied, namely: entropy, fuzziness and ambiguity. First, a methodology based on Granular Computing (GrC), neutrosophic sets and the RBF-NN is presented. The objective of this methodology is to quantify the hesitation produced during the granular compression at the low level of interpretability of the RBF-NN via the use of neutrosophic sets. This study also aims to enhance the disitnguishability and hence the transparency of the initial fuzzy partition. The effectiveness of the proposed methodology is tested against a real case study for the prediction of the properties of heat-treated steels. Secondly, a new Interval Type-2 Radial Basis Function Neural Network (IT2-RBF-NN) is introduced as a new modelling framework. The IT2-RBF-NN takes advantage of the functional equivalence between FLSs of type-1 and the RBF-NN so as to construct an Interval Type-2 Fuzzy Logic System (IT2-FLS) that is able to deal with linguistic uncertainty and perceptions in the RBF-NN rule base. This gave raise to different combinations when optimising the IT2-RBF-NN parameters. Finally, a twofold study for uncertainty assessment at the high-level of interpretability of the RBF-NN is provided. On the one hand, the first study proposes a new methodology to quantify the a) fuzziness and the b) ambiguity at each RU, and during the formation of the rule base via the use of neutrosophic sets theory. The aim of this methodology is to calculate the associated fuzziness of each rule and then the ambiguity related to each normalised consequence of the fuzzy rules that result from the overlapping and to the choice with one-to-many decisions respectively. On the other hand, a second study proposes a new methodology to quantify the entropy and the fuzziness that come out from the redundancy phenomenon during the parameter identification. To conclude this work, the experimental results obtained through the application of the proposed methodologies for modelling two well-known benchmark data sets and for the prediction of mechanical properties of heat-treated steels conducted to publication of three articles in two peer-reviewed journals and one international conference

Explainable clinical decision support system: opening black-box meta-learner algorithm expert's based

Mathematical optimization methods are the basic mathematical tools of all artificial intelligence theory. In the field of machine learning and deep learning the examples with which algorithms learn (training data) are used by sophisticated cost functions which can have solutions in closed form or through approximations. The interpretability of the models used and the relative transparency, opposed to the opacity of the black-boxes, is related to how the algorithm learns and this occurs through the optimization and minimization of the errors that the machine makes in the learning process. In particular in the present work is introduced a new method for the determination of the weights in an ensemble model, supervised and unsupervised, based on the well known Analytic Hierarchy Process method (AHP). This method is based on the concept that behind the choice of different and possible algorithms to be used in a machine learning problem, there is an expert who controls the decisionmaking process. The expert assigns a complexity score to each algorithm (based on the concept of complexity-interpretability trade-off) through which the weight with which each model contributes to the training and prediction phase is determined. In addition, different methods are presented to evaluate the performance of these algorithms and explain how each feature in the model contributes to the prediction of the outputs. The interpretability techniques used in machine learning are also combined with the method introduced based on AHP in the context of clinical decision support systems in order to make the algorithms (black-box) and the results interpretable and explainable, so that clinical-decision-makers can take controlled decisions together with the concept of "right to explanation" introduced by the legislator, because the decision-makers have a civil and legal responsibility of their choices in the clinical field based on systems that make use of artificial intelligence. No less, the central point is the interaction between the expert who controls the algorithm construction process and the domain expert, in this case the clinical one. Three applications on real data are implemented with the methods known in the literature and with those proposed in this work: one application concerns cervical cancer, another the problem related to diabetes and the last one focuses on a specific pathology developed by HIV-infected individuals. All applications are supported by plots, tables and explanations of the results, implemented through Python libraries. The main case study of this thesis regarding HIV-infected individuals concerns an unsupervised ensemble-type problem, in which a series of clustering algorithms are used on a set of features and which in turn produce an output used again as a set of meta-features to provide a set of labels for each given cluster. The meta-features and labels obtained by choosing the best algorithm are used to train a Logistic regression meta-learner, which in turn is used through some explainability methods to provide the value of the contribution that each algorithm has had in the training phase. The use of Logistic regression as a meta-learner classifier is motivated by the fact that it provides appreciable results and also because of the easy explainability of the estimated coefficients