Fuzzy associative matrix

About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.

Scaling of fuzzy controllers using the cross-correlation

Abstract: The paper deals with the optimal adjustment of input scaling factors for fuzzy controllers (FCs). The method is based on the assumption that in the stationary case an optimally adjusted input scaling factor meets a specific statistical input output dependence. A measure for the strength of statistical dependence is the correlation function and the correlation coefficient, respectively. Without loss of generality, the adjustment of input scaling factors using correlation functions is pointed out by means of a single input-single output (SISO)-system. First, the paper deals with the so-called equivalent gain which is closely connected to the cross-correlation of the controller input and the defuzzified controller output. Next, it considers the computation of correlation functions and their representation inside the FC. The paper concludes with an example of a system of fuzzy rules controlling a redundant robot manipulator. >

Falcon: neural fuzzy control and decision systems using FKP and PFKP clustering algorithms

Abstract: Neural fuzzy networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. Examples are the Falcon-ART, and the POPFNN family of networks. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. This correspondence proposes two new networks: Falcon-FKP and Falcon-PFKP. They are extensions of the Falcon-ART network, and aimed to overcome the shortcomings faced by the Falcon-ART network itself, i.e., poor classification ability when the classes of input data are very similar to each other, termination of training cycle depends heavily on a preset error parameter, the fuzzy rule base of the Falcon-ART network may not be consistent Nauck, there is no control over the number of fuzzy rules generated, and learning efficiency may deteriorate by using complementarily coded training data. These deficiencies are essentially inherent to the fuzzy ART, clustering technique employed by the Falcon-ART network. Hence, two clustering techniques- Fuzzy Kohonen Partitioning (FKP) and its pseudo variant PFKP, are synthesized with the basic Falcon structure to compute the fuzzy sets and to automatically derive the fuzzy rules from the training data. The resultant neural fuzzy networks are Falcon-FKP and Falcon-PFKP, respectively. These two proposed networks have a lean and efficient training algorithm and consistent fuzzy rule bases. Extensive simulations are conducted using the two networks and their performances are encouraging when benchmarked against other neural and neural fuzzy systems.

A learning algorithm for tuning fuzzy rules based on the gradient descent method

Abstract: In this paper, we suggest a utility learning algorithm for tuning fuzzy rules by using input-output training data, based on the gradient descent method. The major advantage of this method is that the fuzzy rules or membership functions can be learned without changing the form of the fuzzy rule table used in usual fuzzy controls, so that the case of weak-firing can be avoided, which is different from the conventional learning algorithm. Furthermore, we illustrated the efficiency of the suggested learning algorithm by means of several numerical examples.

Admissibility Analysis and Control Synthesis for T–S Fuzzy Descriptor Systems

Abstract: The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.