Mathematical model of glucose-insulin regulatory system on diabetes mellitus in fuzzy and crisp environment

In this paper we study the mathematical model for glucose insulin regulatory system of diabetes mellitus in fuzzy and crisp environment. To how the behavior of the model is changes in fuzzy environment is discussed briefly. The stability analyses on fuzzy and crisp environments are illustrated. The numerical solutions are found in both cases.

[1]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[2]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

[3]  Tofigh Allahviranloo,et al.  A new method for solving fuzzy linear differential equations , 2011, Computing.

[4]  Eyke Hüllermeier,et al.  An Approach to Modelling and Simulation of Uncertain Dynamical Systems , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[5]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[6]  J. Nieto,et al.  A boundary value problem for second order fuzzy differential equations , 2010 .

[7]  Barnabás Bede,et al.  A note on "two-point boundary value problems associated with non-linear fuzzy differential equations" , 2006, Fuzzy Sets Syst..

[8]  V. Lakshmikantham,et al.  Initial and boundary value problems for fuzzy differential equations , 2003 .

[9]  P. Kloeden,et al.  Metric spaces of fuzzy sets , 1990 .

[10]  Tofigh Allahviranloo,et al.  Fuzzy Laplace transforms , 2009, Soft Comput..

[11]  James J. Buckley,et al.  Fuzzy differential equations , 2000, Fuzzy Sets Syst..

[12]  H. Román-Flores,et al.  On new solutions of fuzzy differential equations , 2008 .

[13]  Osmo Kaleva Fuzzy differential equations , 1987 .

[14]  M Barkhordari Ahmadi,et al.  Fuzzy laplace transform on two order derivative and solving fuzzy two order differential equations , 2009 .

[15]  Y. Chalco-Cano,et al.  Fuzzy differential equations with generalized derivative , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[16]  Imre J. Rudas,et al.  First order linear fuzzy differential equations under generalized differentiability , 2007, Inf. Sci..

[17]  Luciano Stefanini,et al.  Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations , 2012 .

[18]  Barnabás Bede,et al.  Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations , 2005, Fuzzy Sets Syst..

[19]  Luciano Stefanini,et al.  A generalization of Hukuhara difference for interval and fuzzy arithmetic , 2008 .

[20]  Guoqing Liu,et al.  On fuzzy boundary value problems , 2008, Inf. Sci..

[21]  Barnabás Bede,et al.  Generalized differentiability of fuzzy-valued functions , 2013, Fuzzy Sets Syst..

[22]  Tapan Kumar Roy,et al.  First Order Linear Homogeneous Fuzzy Ordinary Differential Equation Based on Lagrange Multiplier Method , 2013 .

[23]  D. Dubois,et al.  Towards fuzzy differential calculus part 3: Differentiation , 1982 .

[24]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

[25]  Rolf Johansson,et al.  Diabetes mellitus modeling and short-term prediction based on blood glucose measurements. , 2009, Mathematical biosciences.