American Journal of Intelligent Systems 2013, 3(1): 33-39 DOI: 10.5923/j.ajis.20130301.05 Fuzzy Time Series Method Based on Multiplicative Neuron Model and Membership Values Erol Egrioglu 1,* , CagdasHakan Aladag 2 , Ufuk Yolcu 3 , Burcin Seyda Corba 1 , Ozge Cagcag 1 1 Department of Statistics, University of OndokuzM ayis, Samsun, 55139, Turkey 2 Department of Statistics, Hacettepe University, Ankara, 06800, Turkey 3 Department of Statistics, Giresun University, Giresun, 28000, Turkey Abstract Many fuzzy time series forecasting methods have been suggested to forecast time series in the literature. Most of these methods use various artificial intelligence methods. The determining of the fuzzy relation is one of the most important stage in fuzzy time series methods. Some methods determine fuzzy relations by using index number of the fuzzy sets. Recently, several methods that use membership values to determine fuzzy relation have been proposed in the literature. In this paper, a new fuzzy time series forecasting algorithm is proposed. The algorithm use fuzzy c-means method in fuzzification stage. The determining of fuzzy relations stage is performed by multiplicative neuron model in proposed algorithm. In the proposed method, membership values are used instead of index number of the fuzzy sets. Three data sets are used to compare proposed method with some other methods in the literature. It is concluded that proposed method outperforms the some other methods in the literature. Keywords Fuzzy Time Series, Forecasting, Multiplicative Neuron Model, Fuzzy C-means 1. Introduction Fuzzy time series methods are based on fuzzy set theory that was proposed by Zadeh[1]. For some time series, the observations of time series can be represented by fuzzy sets. If the observations of the time series are fuzzy sets, traditional time series methods cannot be used. Time series that have got fuzzy observations are called fuzzy time series. The fuzzy time series firstly were defined by Song and Chissom[2]. Moreover, the first fuzzy time series forecasting method was proposed by Song and Chissom[3]. There are two kind of fuzzy time series as time variant and time invariant. The inner relations of time invariant fuzzy time series do not change in time. In generally, fuzzy time series methods have got three stages. These stages are called fuzzification, determining fu zzy relation and deffuzzification, respectively. Various artificial intelligence methods can be used in these stages. Genetic algorithm, particle swarm optimization and fuzzy c-means methods for fuzzification of time series; genetic algorithm, particle swarm optimization and artificial neural networks for determining fuzzy relation and artificial neural networks for defuzzification have been used in the literature. it is known that each stages are very effective on forecasting performance of fuzzy time series. * Corresponding author: erole1977@yahoo.com (ErolEgrioglu) Published online at http://journal.sapub.org/ajis Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved Artificial neural networks were firstly used for determining fuzzy relation by Huarng and Yu[4]. They determined fuzzy relation by using artificial neural networks in first order fuzzy time series forecasting model. Then, Yu and Huarng[5] applied neural networks to fuzzy time series forecasting in bivariate first order fuzzy time series forecasting model. Artificial neural networks were applied to determine fuzzy relation by Egrioglu et al.[6] in bivariate high order fuzzy time series forecasting model. Egrioglu et al. ([7-8]), Aladag et al. ([9-10]) ,Egrioglu et al.[11], Aladağ[12], Yu and Huarng[13] and Yolcu et al.[14]. Egrioglu et al. ([6-7-8]), Aladag et al. ([9-10]), Egrioglu et al.[ 15], Aladağ[16] used index number of fuzzy sets for training artificial neural networks in determining fuzzy relations stage. In these studies, membership values of fuzzy sets are not taken into consideration. Yu and Huarng[13] and Yolcu et al.[14] used membership values of fuzzy sets for training artificial neural networks in determining fuzzy relations stage. Aladağ[16] different from others since it used multiplicative neuron model neural network instead of multilayer perceptron neural network. The multiplicative neuron model neural network was use to determine fuzzy relation of seasonal fuzzy time seires in Aladağ S. et al. [12]. In this study, novel fuzzy time series method is proposed. Proposed method use fuzzy c-means clustering in fuzzification stage and multiplicative neuron model neural network in determining fuzzy relations stage. Particle swarm optimization method is applied for training multiplicative neuron model neural network. Fuzzy c-means, multiplicative neuron model neural network and particle swarm