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

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

Automatic synthesis of fuzzy systems: An evolutionary overview with a genetic programming perspective

Studies in Evolutionary Fuzzy Systems (EFSs) began in the 90s and have experienced a fast development since then, with applications to areas such as pattern recognition, curve‐fitting and regression, forecasting and control. An EFS results from the combination of a Fuzzy Inference System (FIS) with an Evolutionary Algorithm (EA). This relationship can be established for multiple purposes: fine‐tuning of FIS's parameters, selection of fuzzy rules, learning a rule base or membership functions from scratch, and so forth. Each facet of this relationship creates a strand in the literature, as membership function fine‐tuning, fuzzy rule‐based learning, and so forth and the purpose here is to outline some of what has been done in each aspect. Special focus is given to Genetic Programming‐based EFSs by providing a taxonomy of the main architectures available, as well as by pointing out the gaps that still prevail in the literature. The concluding remarks address some further topics of current research and trends, such as interpretability analysis, multiobjective optimization, and synthesis of a FIS through Evolving methods

Survey on Neuro-Fuzzy systems and their applications in technical diagnostics and measurement

Both fuzzy logic, as the basis of many inference systems, and Neural Networks, as a powerful computational model for classification and estimation, have been used in many application fields since their birth. These two techniques are somewhat supplementary to each other in a way that what one is lacking of the other can provide. This led to the creation of Neuro-Fuzzy systems which utilize fuzzy logic to construct a complex model by extending the capabilities of Artificial Neural Networks. Generally speaking all type of systems that integrate these two techniques can be called Neuro-Fuzzy systems. Key feature of these systems is that they use input-output patterns to adjust the fuzzy sets and rules inside the model. The paper reviews the principles of a Neuro-Fuzzy system and the key methods presented in this field, furthermore provides survey on their applications for technical diagnostics and measurement. © 2015 Elsevier Ltd

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

Learning and identification of fuzzy systems

This thesis concentrates on learning and identification of fuzzy systems, and this thesis is composed about learning fuzzy systems from data for regression and function approximation by constructing complete, compact, and consistent fuzzy systems. Fuzzy systems are prevalent to solve pattern recognition problems and function approximation problems as a result of the good knowledge representation. With the development of fuzzy systems, a lot of sophisticated methods based on them try to completely solve pattern recognition problems and function approximation problems by constructing a great diversity of mathematical models. However, there exists a conflict between the degree of the interpretability and the accuracy of the approximation in general fuzzy systems. Thus, how to properly make the best compromise between the accuracy of the approximation and the degree of the interpretability in the entire system is a significant study of the subject.The first work of this research is concerned with the clustering technique on constructing fuzzy models in fuzzy system identification, and this method is a part of clustering based learning of fuzzy systems. As the determination of the proper number of clusters and the appropriate location of clusters is one of primary considerations on constructing an effectively fuzzy model, the task of the clustering technique aims at recognizing the proper number of clusters and the appropriate location as far as possible, which gives a good preparation for the construction of fuzzy models. In order to acquire the mutually exclusive performance by constructing effectively fuzzy models, a modular method to fuzzy system identification based on a hybrid clustering-based technique has been considered. Due to the above reasons, a hybrid clustering algorithm concerning input, output, generalization and specialization has hence been introduced in this work. Thus, the primary advantage of this work is the proposed clustering technique integrates a variety of clustering properties to positively identify the proper number of clusters and the appropriate location of clusters by carrying out a good performance of recognizing the precise position of each dataset, and this advantage brings fuzzy systems more complete.The second work of this research is an extended work of the first work, and two ways to improve the original work have been considered in the extended work, including the pruning strategy for simplifying the structure of fuzzy systems and the optimization scheme for parameters optimization. So far as the pruning strategy is concerned, the purpose of which aims at refining rule base by the similarity analysis of fuzzy sets, fuzzy numbers, fuzzy membership functions or fuzzy rules. By other means, through the similarity analysis of which, the complete rules can be kept and the redundant rules can be reduced probably in the rule base of fuzzy systems. Also, the optimization scheme can be regarded as a two-layer parameters optimization in the extended work, because the parameters of the initial fuzzy model have been fine tuning by two phases gradation on layer. Hence, the extended work primarily puts focus on enhancing the performance of the initial fuzzy models toward the positive reliability of the final fuzzy models. Thus, the primary advantage of this work consists of the simplification of fuzzy rule base by the similarity-based pruning strategy, as well as more accuracy of the optimization by the two-layer optimization scheme, and these advantages bring fuzzy systems more compact and precise.So far as a perfect modular method for fuzzy system identification is concerned, in addition to positively solve pattern recognition problems and function approximation problems, it should primarily comprise the following features, including the well-understanding interpretability, low-degree dimensionality, highly reliability, stable robustness, highly accuracy of the approximation, less computational cost, and maximum performance. However, it is extremely difficult to meet all of these conditions above. Inasmuch as attaining the highly achievement from the features above as far as possible, the research works of this thesis try to present a modular method concerning a variety of requirements to fuzzy systems identification.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

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

Sistemas granulares evolutivos

Orientador: Fernando Antonio Campos GomideTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente tem-se observado um crescente interesse em abordagens de modelagem computacional para lidar com fluxos de dados do mundo real. Métodos e algoritmos têm sido propostos para obtenção de conhecimento a partir de conjuntos de dados muito grandes e, a princípio, sem valor aparente. Este trabalho apresenta uma plataforma computacional para modelagem granular evolutiva de fluxos de dados incertos. Sistemas granulares evolutivos abrangem uma variedade de abordagens para modelagem on-line inspiradas na forma com que os humanos lidam com a complexidade. Esses sistemas exploram o fluxo de informação em ambiente dinâmico e extrai disso modelos que podem ser linguisticamente entendidos. Particularmente, a granulação da informação é uma técnica natural para dispensar atenção a detalhes desnecessários e enfatizar transparência, interpretabilidade e escalabilidade de sistemas de informação. Dados incertos (granulares) surgem a partir de percepções ou descrições imprecisas do valor de uma variável. De maneira geral, vários fatores podem afetar a escolha da representação dos dados tal que o objeto representativo reflita o significado do conceito que ele está sendo usado para representar. Neste trabalho são considerados dados numéricos, intervalares e fuzzy; e modelos intervalares, fuzzy e neuro-fuzzy. A aprendizagem de sistemas granulares é baseada em algoritmos incrementais que constroem a estrutura do modelo sem conhecimento anterior sobre o processo e adapta os parâmetros do modelo sempre que necessário. Este paradigma de aprendizagem é particularmente importante uma vez que ele evita a reconstrução e o retreinamento do modelo quando o ambiente muda. Exemplos de aplicação em classificação, aproximação de função, predição de séries temporais e controle usando dados sintéticos e reais ilustram a utilidade das abordagens de modelagem granular propostas. O comportamento de fluxos de dados não-estacionários com mudanças graduais e abruptas de regime é também analisado dentro do paradigma de computação granular evolutiva. Realçamos o papel da computação intervalar, fuzzy e neuro-fuzzy em processar dados incertos e prover soluções aproximadas de alta qualidade e sumário de regras de conjuntos de dados de entrada e saída. As abordagens e o paradigma introduzidos constituem uma extensão natural de sistemas inteligentes evolutivos para processamento de dados numéricos a sistemas granulares evolutivos para processamento de dados granularesAbstract: In recent years there has been increasing interest in computational modeling approaches to deal with real-world data streams. Methods and algorithms have been proposed to uncover meaningful knowledge from very large (often unbounded) data sets in principle with no apparent value. This thesis introduces a framework for evolving granular modeling of uncertain data streams. Evolving granular systems comprise an array of online modeling approaches inspired by the way in which humans deal with complexity. These systems explore the information flow in dynamic environments and derive from it models that can be linguistically understood. Particularly, information granulation is a natural technique to dispense unnecessary details and emphasize transparency, interpretability and scalability of information systems. Uncertain (granular) data arise from imprecise perception or description of the value of a variable. Broadly stated, various factors can affect one's choice of data representation such that the representing object conveys the meaning of the concept it is being used to represent. Of particular concern to this work are numerical, interval, and fuzzy types of granular data; and interval, fuzzy, and neurofuzzy modeling frameworks. Learning in evolving granular systems is based on incremental algorithms that build model structure from scratch on a per-sample basis and adapt model parameters whenever necessary. This learning paradigm is meaningful once it avoids redesigning and retraining models all along if the system changes. Application examples in classification, function approximation, time-series prediction and control using real and synthetic data illustrate the usefulness of the granular approaches and framework proposed. The behavior of nonstationary data streams with gradual and abrupt regime shifts is also analyzed in the realm of evolving granular computing. We shed light upon the role of interval, fuzzy, and neurofuzzy computing in processing uncertain data and providing high-quality approximate solutions and rule summary of input-output data sets. The approaches and framework introduced constitute a natural extension of evolving intelligent systems over numeric data streams to evolving granular systems over granular data streamsDoutoradoAutomaçãoDoutor em Engenharia Elétric