A gradient-descent-based approach for transparent linguistic interface generation in fuzzy models

Linguistic interface is a group of linguistic terms or fuzzy descriptions that describe variables in a system utilizing corresponding membership functions. Its transparency completely or partly decides the interpretability of fuzzy models. This paper proposes a GRadiEnt-descEnt-based Transparent lInguistic iNterface Generation (GREETING) approach to overcome the disadvantage of traditional linguistic interface generation methods where the consideration of the interpretability aspects of linguistic interface is limited. In GREETING, the widely used interpretability criteria of linguistic interface are considered and optimized. The numeric experiments on the data sets from University of California, Irvine (UCI) machine learning databases demonstrate the feasibility and superiority of the proposed GREETING method. The GREETING method is also applied to fuzzy decision tree generation. It is shown that GREETING generates better transparent fuzzy decision trees in terms of better classification rates and comparable tree sizes.

Intelligent motion control for linear piezoelectric ceramic motor drive

Since the dynamic characteristics of a linear piezoelectric ceramic motor (LPCM) are highly nonlinear and time varying, it is difficult to design a suitable motor drive and position controller that realizes accurate position control at all time. This study investigates a double-inductance double-capacitance (LLCC) resonant driving circuit and a sliding-mode fuzzy-neural-network control (SMFNNC) system for the motion control of an LPCM. First, the motor structure and LLCC driving circuit of an LPCM are introduced. The LLCC resonant inverter is designed to operate at an optimal switching frequency such that the output voltage will not be influenced by the variation of quality factor. Moreover, a SMFNNC system is designed to achieve favorable tracking performance without precise dynamic models being controlled. All adaptive learning algorithms in the SMFNNC system are derived in the sense of Lyapunov stability analysis, so that system-tracking stability can be guaranteed in the closed-loop system. The effectiveness of the proposed driving circuit and control system is verified by experimental results.

Efficient Learning Algorithms for Three-Layer Regular Feedforward Fuzzy Neural Networks

A key step of using gradient descend methods to develop learning algorithms of a regular feedforward fuzzy neural network (FNN) is to differentiate max--min functions, which contain max and min operations. The paper aims at several objectives. First, investigate further the differentiation of max--min functions. Second, employ general fuzzy numbers, which include triangular and trapezoidal fuzzy numbers as special cases to define a three-layer regular FNN. The general fuzzy numbers related can be approximately determined by their corresponding finite level sets. So, we can approximately represent the input-output (I/O) relationship of the regular FNN as functions of the endpoints of all finite level sets. Third, a fuzzy back-propagation algorithm is presented. And to speed up the convergence of the learning algorithm, a fuzzy conjugate gradient algorithm for fuzzy weights and biases is developed, furthermore, the convergence of the algorithm is analyzed, systematically. Finally, some real simulations demonstrate the efficiency of our learning algorithms. The regular FNN is applied to the approximate realization of fuzzy inference rules and fuzzy functions defined on given compact sets.

Dynamical properties of min-max networks

In this paper we study the dynamical behavior of a class of neural networks where the local transition rules are max or min functions. We prove that sequential updates define dynamics which reach the equilibrium in O(n2) steps, where n is the size of the network. For synchronous updates the equilibrium is reached in O(n) steps. It is shown that the number of fixed points of the sequential update is at most n. Moreover, given a set of p < or = n vectors, we show how to build a network of size n such that all these vectors are fixed points.