Abstract—An additive fuzzy system comprising m rules with n inputs and p outputs in each rule has at least ( ) 1 2 2 + + p n m parameters needing to be tuned. The system consists of a large number of if-then fuzzy rules and takes a long time to tune its parameters especially in the case of a large amount of training data samples. In this paper, a new learning strategy is investigated to cope with this obstacle. Parameters that tend toward constant values at the learning process are initially fixed and they are not tuned till the end of the learning time. Experiments based on applications of the additive fuzzy system in function approximation demonstrate that the proposed approach reduces the learning time and hence improves convergence speed considerably. Keywords—Additive fuzzy system, improving convergence, parameter learning process, unsupervised learning. I. THE ADDITIVE FUZZY SYSTEM AND İTS PARAMETERS HE additive fuzzy system or the so-called Standard Additive Model (SAM) is a particular type of fuzzy systems proposed by Kosko [1, 3, 5, 6]. A fuzzy system F : p R n R → stores m if-then rules and can uniformly approximate continuous and bounded measurable functions in the compact domain [2]. This approximation theorem allows any choice of if-part fuzzy sets n R j A ⊂ . It also allows any choice of the then-part fuzzy sets p R j B ⊂ because the system uses only the centroid j c and volume j V of j B to compute the output () x F from the vector input n R x ∈ . Thi Nguyen was with the Centre for GIS, School of Geography and Environmental Science, Monash University, Victoria, Australia (e-mail: thi.nguyenthanh@gmail.com). Lee Gordon-Brown is with the Department of Econometrics and Business Statistics, Monash University, Victoria, Australia. Jim Peterson and Peter Wheeler are with the Centre for GIS, School of Geography and Environmental Science, Monash University, Victoria, Australia. () () () () ∑ = = ∑ = ∑ = = ∑ = = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ m j j c x j p m j j V x j a j w m j j c j V x j a j w m j j B x j a j w Centroid F(x) 1 1 1 1 (1) (a) (b) Fig. 1 (a) A parallel structure of SAM. Each input fires each fuzzy rule to some degree to compute F(x) (b) Fuzzy rules define patches in the input-output space The fuzzy system F : p R n R → covers the graph of an approximand f with m fuzzy rule patches of the form p R n R j B j A × ⊂ × or “If j A X = then j B Y = ”. If-part set n R j A ⊂ has joint set function j a : [ ] 1 , 0 → n R that factors: ) n (x n j )...a (x j a (x) j a 1 1 = . Then-part fuzzy set Improving Convergence of Parameter Tuning Process of the Additive Fuzzy System by New Learning Strategy Thi Nguyen, Lee Gordon-Brown, Jim Peterson, and Peter Wheeler T World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:2, No:9, 2008 2929 International Scholarly and Scientific Research & Innovation 2(9) 2008 scholar.waset.org/1307-6892/6593 International Science Index, Computer and Information Engineering Vol:2, No:9, 2008 waset.org/Publication/6593