Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework

AbstractIn this paper we propose a multi-objective evolutionary algorithm to generate Mamdani fuzzy rule-based systems with different good trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we introduce the concepts of virtual and concrete rule bases: the former is defined on linguistic variables, all partitioned with a fixed maximum number of fuzzy sets, while the latter takes into account, for each variable, a number of fuzzy sets as determined by the specific partition granularity of that variable. We exploit a chromosome composed of two parts, which codify the variables partition granularities, and the virtual rule base, respectively. Genetic operators manage virtual rule bases, whereas fitness evaluation relies on an appropriate mapping strategy between virtual and concrete rule bases. The algorithm has been tested on two real-world regression problems showing very promising results

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

An overview of recent distributed algorithms for learning fuzzy models in Big Data classification

AbstractNowadays, a huge amount of data are generated, often in very short time intervals and in various formats, by a number of different heterogeneous sources such as social networks and media, mobile devices, internet transactions, networked devices and sensors. These data, identified as Big Data in the literature, are characterized by the popular Vs features, such as Value, Veracity, Variety, Velocity and Volume. In particular, Value focuses on the useful knowledge that may be mined from data. Thus, in the last years, a number of data mining and machine learning algorithms have been proposed to extract knowledge from Big Data. These algorithms have been generally implemented by using ad-hoc programming paradigms, such as MapReduce, on specific distributed computing frameworks, such as Apache Hadoop and Apache Spark. In the context of Big Data, fuzzy models are currently playing a significant role, thanks to their capability of handling vague and imprecise data and their innate characteristic to be interpretable. In this work, we give an overview of the most recent distributed learning algorithms for generating fuzzy classification models for Big Data. In particular, we first show some design and implementation details of these learning algorithms. Thereafter, we compare them in terms of accuracy and interpretability. Finally, we argue about their scalability

Một phương pháp sinh hệ luật mờ Mamdani cho bài toán hồi qui với ngữ nghĩa Đại số gia tử

In this paper, we propose an evolution algorithm to generate Mamdani Fuzzy Rule-based Systems (MFRBS) with different trade-off between complexity and accuracy. The algorithm was developed taking the idea of the schema evolution (2+2)M-PAES which has been proposed in [6]. The main novelty of the algorithm is to learn concurrently rule bases, fuzzy partitions and linguistic terms along with their fuzzy sets using hedge algebra (HA) methodology. The algorithm allows to generate rules from pattern data utilizing new information of partitions and fuzzy sets in the same individual. In addition, we propose a new method for encoding individuals that can be realized in the hedge algebra approach to solve this problem. The computer simulation is carried out with six standard regression problems in [10] accepted by the research community and the obtained results show that the MFRBSs generated by the proposed algorithm are better than those examined in [8] with respect to two objectives, the complexity and the accuracy.Trong bài báo này, chúng tôi đề xuất một thuật toán tiến hóa sinh các hệ luật mờ Mamdani (MFRBS) đạt được mức độ thỏa hiệp khác nhau giữa hai mục tiêu độ phức tạp và độ chính xác. Thuật toán phát triển lấy ý tưởng từ thuật toán (2+2)M-PAES đề xuất trong [6] và [8]. Điểm mới của thuật toán là học đồng thời cơ sở luật, các phân hoạch mờ và các hạng từ ngôn ngữ cùng với các tập mờ của chúng sử dụng phương pháp đại số gia tử. Thuật toán cho phép sinh các luật từ mẫu dữ liệu sử dụng thông tin mới nhất của các phân hoạch và các tập mờ trong cùng thế hệ. Thêm vào đó, chúng tôi đề xuất một phương pháp mã hóa các cá thể mới theo hướng tiếp cận đại số gia tử để giải quyết bài toán toán này. Thuật toán được thử nghiệm trên sáu bài toán hồi qui mẫu lấy từ thực tế được cộng đồng nghiên cứu chấp nhận, kết quả cho thấy thuật toán sinh ra các hệ luật mờ tốt hơn so với thuật toán trong [8] trên cả hai mục tiêu độ phức tạp và độ chính xác, và sinh ra mặt xấp xỉ tối ưu Pareto trội hơn trên tất cả các bài toán

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

Fuzzy qualitative trigonometry

AbstractThis paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalized fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyze general trigonometry-related physical systems from an artificial intelligence perspective.Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks

A single-objective and a multi-objective genetic algorithm to generate accurate and interpretable fuzzy rule based classifiers for the analysis of complex financial data

Nowadays, organizations deal with rapidly increasing amount of data that is stored in their databases. It has therefore become of crucial importance for them to identify the necessary patterns in these large databases to turn row data into valuable and actionable information. By exploring these important datasets, the organizations gain competitive advantage against other competitors, based on the assumption that the added value of Knowledge Management Systems strength is first and foremost to facilitate the decision making process. Especially if we consider the importance of knowledge in the 21st century, data mining can be seen as a very effective tool to explore the essential data that foster competitive gain in a changing environment. The overall aim of this study is to design the rule base component of a fuzzy rule-based system (FRBS) through the use of genetic algorithms. The main objective is to generate accurate and interpretable models of the data trying to overcome the existing tradeoff between accuracy and interpretability. We propose two different approaches: an accuracy-driven single-objective genetic algorithm, and a three-objective genetic algorithm that produce a Pareto front approximation, composed of classifiers with different tradeoffs between accuracy and complexity. The proposed approaches have been compared with two other systems, namely a rule selection single-objective algorithm, and a three-objective algorithm. The latter has been developed by the University of Pisa and is able to generate the rule base, while simultaneously learning the definition points of the membership functions, by taking into account both the accuracy and the interpretability of the final model

Metodología para medir y evaluar las capacidades tecnológicas de innovación aplicando sistemas de lógica difusa caso fábricas de software

El presente trabajo expone una metodología para medir y evaluar las Capacidades Tecnológicas de Innovación (CTI) y su impacto en el desempeño de fábricas de software. Aunque la medición del nivel de CTI es un proceso complejo, la metodología propuesta enfrenta este desafío caracterizando las CIT en capacidades constitutivas según la base de conocimiento establecida por empresarios y expertos en el tema, la herramienta aplicada para calcular el nivel de CIT en una fábrica de software fue lógica difusa, aplicando conjuntos difusos del tipo integral Mamdani. La metodología fue verificada y validada con la industria Antioqueña. Actualmente no existe ninguna herramienta formal para medir y evaluar las CTI en una industria tan especifica como la del software, que presenta dinámicas de comportamiento y crecimiento trascendentales, basadas en la innovación constante. Por tal motivo se adelantó la investigación en búsqueda de aportar al desarrollo del conocimiento, la ciencia y el desarrollo del país.Maestrí