Model fuzzy untuk data fuzzy time series dan aplikasinya di bidang finansial

Fuzzy Model for Fuzzy Time Series Data and Its Application in Finance By Agus Maman Abadi 06/09-I/2021/PS Fuzzy time series is a dynamical process of linguistic variables whose fuzzy sets as its linguistic values. The uniqueness of fuzzy time series model are that the model can formulate problems based on expert knowledge only or hybrid of expert knowledge and empirical data In the modeling fuzzy time series data, previous researchers define fuzzy set using discrete membership function. Then Mamdani composition is applied to construct fuzzy relations based on training data. Optimization of the model is done by clustering of fuzzy relations to a group and then defuzzification is applied. This fuzzy relation is used to predict real data or fuzzy sets. In this research, new procedures to modeling fuzzy for fuzzy time series data were established. The procedures consist of constructing fuzzy relations based on composition and individual based inferences using operator s-norm and t-norm, selecting input variables, designing complete fuzzy relations, and constructing optimal fuzzy relations. The fuzzy relations designed by composition based inferences are union of fuzzy relations based on training data. Then this fuzzy relations are used to predict fuzzy set output using operator sup-t. Furthermore, in individual based inferences, for a fuzzy set input, every fuzzy relation resulted from training data determines fuzzy set output using operator sup-t. Then fuzzy set output of fuzzy model is union of fuzzy set output resulted from every fuzzy relation using operator tnorm. The construction of fuzzy relations based on composition and individual based inferences using operator s-norm and t-norm is generalization of construction of fuzzy relations introduced by Song and Chissom. Selection of input variables is done by singular value decomposition method of sensitivity matrix. Columns of this matrix are sensitivity of each input variable. This method is used to determine significant input variables. Position of the significant input variables is equivalent to the position of entry “1” of permutation matrix. Based on the significant input variables, complete fuzzy relations are designed by degree of fuzzy relation method. This method is generalization of Wang’s method. Then singular value decomposition method is applied to firing strength matrix to choose optimal fuzzy relations from complete fuzzy relations. Then the optimal fuzzy relations are used to design fuzzy model. The methods are applied to forecast inflation rate and interest rate of Bank Indonesia certificate. Forecasting inflation rate and interest rate of Bank Indonesia certificate using method of degree of fuzzy relation gives better accuracy than that using standard method for conventional time series model. Then forecasting inflation rate and interest rate of Bank Indonesia certificate using singular value decomposition method gives better accuracy than that using standard method for conventional time series mode