The gradient-type self-organizing fuzzy system with singleton output for multi-input fuzzy variables using I/O data

Fuzzy logic has been known widely in managing imprecise and uncertain situations. But if we design and implement a fuzzy system, we should have identified it through trial and error many times. So, in order to solve a problem like this, on the whole, two types of self-organizing fuzzy systems have been usually proposed. One is the fusion method like fuzzy neural nets or fuzzy genetic algorithms, the other is to use a kind of gradient descent method. The former has a problem in that we must well understand the basic concept of two information processing schemes. The latter has also a problem in that the processing time slows, because the number of fuzzy rules increases in proportion to the number of functions whenever a fuzzy membership function is created. Thus, we have suggested a gradient type self-organizing fuzzy system without using the fusion method of other information processing schemes like neural networks or genetic algorithms. The characteristics of this system are that the conclusion part of the fuzzy rules consists of singleton output type. This method can avoid the explosive increase in fuzzy rules and minimize the number of membership functions. However, this algorithm has a little latency time in learning. This paper discusses how to improve these problems. Several numerical examples and the experiment of a cart-pole control system show that the advanced method has not only less numbers of fuzzy rules and membership functions but also short learning cycles to satisfy any desired accuracy.