A possibilistic approach to latent structure analysis for symmetric fuzzy data.

In many situations the available amount of data is huge and can be intractable. When the data set is single valued, latent structure models are recognized techniques, which provide a useful compression of the information. This is done by considering a regression model between observed and unobserved (latent) fuzzy variables. In this paper, an extension of latent structure analysis to deal with fuzzy data is proposed. Our extension follows the possibilistic approach, widely used both in the cluster and regression frameworks. In this case, the possibilistic approach involves the formulation of a latent structure analysis for fuzzy data by optimization. Specifically, a non-linear programming problem in which the fuzziness of the model is minimized is introduced. In order to show how our model works, the results of two applications are given.Latent structure analysis, symmetric fuzzy data set, possibilistic approach.

Statistical Genetic Interval-Valued Type-2 Fuzzy System and its Application

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and a new probability type reduced reasoning method for the interval-valued fuzzy logic system are proposed in this thesis. In order to optimize this particle system’s performance, we adopt genetic algorithm (GA) to adjust parameters. The applications for the new system are performed and results have shown that the developed method is more accurate and robust to design a reliable fuzzy logic system than type-1 method and the computation of our proposed method is more efficient

Modeling of complex-valued Wiener systems using B-spline neural network

In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate Bspline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss–Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches

A randomized neural network for data streams

© 2017 IEEE. Randomized neural network (RNN) is a highly feasible solution in the era of big data because it offers a simple and fast working principle in processing dynamic and evolving data streams. This paper proposes a novel RNN, namely recurrent type-2 random vector functional link network (RT2McRVFLN), which provides a highly scalable solution for data streams in a strictly online and integrated framework. It is built upon the psychologically inspired concept of metacognitive learning, which covers three basic components of human learning: what-to-learn, how-to-learn, and when-to-learn. The what-to-learn selects important samples on the fly with the use of online active learning scenario, which renders our algorithm an online semi-supervised algorithm. The how-to-learn process combines an open structure of evolving concept and a randomized learning algorithm of random vector functional link network (RVFLN). The efficacy of the RT2McRVFLN has been numerically validated through two real-world case studies and comparisons with its counterparts, which arrive at a conclusive finding that our algorithm delivers a tradeoff between accuracy and simplicity

Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics