An Improved Learning Algorithm of Fuzzy Inference Systems Using Vector Quantization

Learning Algorithms for Fuzzy Inference Systems Using Vector Quantization

“…Learning Algorithm B using Algorithm Center (c) is introduced as follows [16,17]: Step 1: Initialize()…”

“…These methods are the ones determining only the antecedent parameters by VQ. Therefore, we introduced generalized inverse matrix (GIM) to determine the initial assignment of weight parameters for the consequent part of fuzzy rules as the fourth method and showed the effectiveness in the previous paper [16,17]. In this paper, improved methods for learning process of SDM in learning methods using VQ, GIM, and SDM are introduced and show that the method is superior in the number of rules to other methods in numerical simulations.…”

“…Some novel methods on them have been developed which (1) generate fuzzy rules one by one starting from any number of rules, or reduce fuzzy rules one by one starting from a sufficiently large number of rules [2]; (2) use genetic algorithm (GA) and particle swarm optimization (PSO) to determine fuzzy systems [3]; (3) use fuzzy inference systems composed of a small number of input rule modules, such as single input rule modules (SIRMs) and double input rule modules (DIRMs) methods [9,10]; and (4) use a self-organization or a vector quantization technique to determine the initial assignment of parameters [11][12][13][14][15]19]. Specifically, it is known that learning methods using vector quantization (VQ) and steepest descent method (SDM) are superior in the number of rules (parameters) to other methods [16,19]. So, why is it effective to combine VQ with SDM in fuzzy modeling?…”

“…As described above, many methods are not necessarily effective models because of the difficulty of learning accompanying the increase of the input dimension and the number of rules and the low accuracy. On the other hand, the method combining VQ with SDM is possible to efficiently conduct learning of SDM by arranging suitably the initial parameters of fuzzy rules using VQ [1,16]. However, since VQ is unsupervised learning, it is easy to reflect the input part of learning data, but how to capture output information in learning is difficult.…”

“…With their studies, the first learning method is the one using VQ only in determining the initial parameters of the antecedent part of fuzzy rules using input part of learning data [1,[11][12][13][14]. The second method is the one determining the same parameter using input/output parts of learning data [15,19]. Further, the third method is one iterating learning process of VQ and SDM for the second method.…”