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

A Genetic-Programming-Based Approach for the Learning of Compact Fuzzy Rule-Based Classification Systems

In the design of an interpretable fuzzy rule-based classification system (FRBCS) the precision as much as the simplicity of the extracted knowledge must be considered as objectives. In any inductive learning algorithm, when we deal with problems with a large number of features, the exponential growth of the fuzzy rule search space makes the learning process more difficult. Moreover it leads to an FRBCS with a rule base with a high cardinality. In this paper, we propose a genetic-programming-based method for the learning of an FRBCS, where disjunctive normal form (DNF) rules compete and cooperate among themselves in order to obtain an understandable and compact set of fuzzy rules, which presents a good classification performance with high dimensionality problems. This proposal uses a token competition mechanism to maintain the diversity of the population. The good results obtained with several classification problems support our proposal.Spanish Ministry of Science and Technology TIN-2005-08386-C05-03 and TIN-2005-08386-C05-0

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Knowledge Extraction in Video Through the Interaction Analysis of Activities

Video is a massive amount of data that contains complex interactions between moving objects. The extraction of knowledge from this type of information creates a demand for video analytics systems that uncover statistical relationships between activities and learn the correspondence between content and labels. However, those are open research problems that have high complexity when multiple actors simultaneously perform activities, videos contain noise, and streaming scenarios are considered. The techniques introduced in this dissertation provide a basis for analyzing video. The primary contributions of this research consist of providing new algorithms for the efficient search of activities in video, scene understanding based on interactions between activities, and the predicting of labels for new scenes

Algorithmic and Statistical Perspectives on Large-Scale Data Analysis

In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved worst-case algorithms that are useful for large-scale scientific and Internet data analysis problems. In this chapter, I will describe two recent examples---one having to do with selecting good columns or features from a (DNA Single Nucleotide Polymorphism) data matrix, and the other having to do with selecting good clusters or communities from a data graph (representing a social or information network)---that drew on ideas from both areas and that may serve as a model for exploiting complementary algorithmic and statistical perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors, "Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201