Parameter Estimation in a Fuzzy Logistic Growth Model
(The 6th Annual Basic Science International Conference Proceedings, Basic 2016 – Malang)
Muhammad Ahsar K. 1, 2, a), Agus Yodi Gunawan 2, Kuntjoro Adji Sidarto 2, and Mochamad Apri 2
1 Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University, Banjarbaru, Indonesia.
2 Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia.
a) m_ahsar@yahoo.com
ABSTRACT
Measurement from experiments often consists of uncertainty. This is possibly either due to the limitations of available data or the external-internal changes in system. For example, the growth model of certain cell population, which may be modeled by a logistic growth model, is strongly influenced by biological and chemical reactions in cells. These conditions affect the system having uncertainty in the system variables and/or parameters. In this work, we consider a logistic model which accommodates the uncertainty in the number of populations, in the terms of fuzzy variables. We apply concepts of fuzzy arithmetic to the model, which leads to -cut deterministic models with extra numbers of equations. We then solve the -cut deterministic equations using the Runge-Kutta Method and estimate the parameters using the Nonlinear Least-Square Method.
KEYWORDS: fuzzy variables, fuzzy arithmetic, -cut deterministic models, fuzzy logistic growth models.
REFERENCES
- Apri M., Tackling Complex Models in Systems Biology, Thesis, Wegeningen University, Wegeningen, 2013.
- Hanss M., Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, Springer, Stuttgart, 2004.
- Massad E. dkk., Fuzzy Logic in Action: Applications in Epidemiology and Beyond, Springer-Verlag Berlin Heidelberg, Berlin, 2008.
- Zadeh L. A., Fuzzy Sets, Information and Control, 8 (1965), 338 – 353.
