A fuzzy mathematical model of West Java population with logistic growth model

Indonesian Operations Research Association - International Conference on Operations Research 2017

Nurkholipah, N.S.^1 ; Amarti, Z.^1 ; Anggriani, N.^2 ; Supriatna, A.K.^2

Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia^1

Departement of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia^2

关键词: Dependent variables;    Fourth-order runge-kutta;    Fuzzy initial values;    Independent variables;    Logistic differential equations;    Logistic growth model;    Mean absolute percentage error;    Triangle fuzzy numbers;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/332/1/012035/pdf
DOI  :  10.1088/1757-899X/332/1/012035

来源: IOP

【 摘 要 】

In this paper we develop a mathematics model of population growth in the West Java Province Indonesia. The model takes the form as a logistic differential equation. We parameterize the model using several triples of data, and choose the best triple which has the smallest Mean Absolute Percentage Error (MAPE). The resulting model is able to predict the historical data with a high accuracy and it also able to predict the future of population number. Predicting the future population is among the important factors that affect the consideration is preparing a good management for the population. Several experiment are done to look at the effect of impreciseness in the data. This is done by considering a fuzzy initial value to the crisp model assuming that the model propagates the fuzziness of the independent variable to the dependent variable. We assume here a triangle fuzzy number representing the impreciseness in the data. We found that the fuzziness may disappear in the long-term. Other scenarios also investigated, such as the effect of fuzzy parameters to the crisp initial value of the population. The solution of the model is obtained numerically using the fourth-order Runge-Kutta scheme.