TY - JOUR AU - Mondal, Sankar Prasad AU - Khan, Najeeb Alam AU - Razzaq, Oyoon Abdul AU - Roy, Tapan Kumar PY - 2018 TI - Adaptive strategies for system of fuzzy differential equation: application of arms race model JO - Journal of Mathematics and Computer Science SP - 192--205 VL - 18 IS - 2 AB - The paper presents adaptive stratagems to scrutinize the system of first order fuzzy differential equations (SFDE) in two modes, fuzzy and in crisp sense. Its fuzzy solutions are carried out using two approaches, namely, Zadeh's extension principle and generalized Hukuhara derivative (gH-derivative). While, different defuzzification techniques; central of area method (COA), bisector of area method (BOA), largest of maxima (LOM), smallest of maxima (SOM), mean of maxima (MOM), regular weighted point method (RWPM), graded mean integration value (GMIV), and center of approximated interval (COAI), are employed to discuss the crisp solutions. Moreover, the arms race model (ARM), which have a significant implication in international military planning, are pragmatic examples of system of first order differential equations, but not studied in fuzzy sense, hitherto. Therefore, ARM is re-established and studied here with fuzzy numbers to estimate its uncertain parameters, as a practical utilization of SFDE. Additionally, an illustrative example of ARM is undertaken to clarify the appropriateness of the proposed approaches. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.018.02.07 DO - 10.22436/jmcs.018.02.07 ID - Mondal2018 ER - TY - JOUR TI - On fuzzy solutions for heat equation based on generalized Hukuhara differentiability AU - T. Allahviranloo AU - Z. Gouyandeh AU - A. Armand AU - A. Hasanoglu JO - Fuzzy Sets and Systems PY - 2015 DA - 2015// VL - 265 ID - Allahviranloo2015 ER - TY - JOUR TI - Fuzzy modelling in population dynamics AU - L. C. Barros AU - R. C. Bassanezi AU - P. A. Tonelli JO - Ecol. Model. PY - 2000 DA - 2000// VL - 128 ID - Barros2000 ER - TY - JOUR TI - Friction model by using fuzzy differential equations AU - B. Bede AU - I. J. Rudas AU - J. Fodor JO - Lecture Notes in Comput. Sci. PY - 2007 DA - 2007// VL - 4529 ID - Bede2007 ER - TY - JOUR TI - Generalized differentiability of fuzzy-valued functions AU - B. Bede AU - L. Stefanini JO - Fuzzy Sets and Systems PY - 2013 DA - 2013// VL - 230 ID - Bede2013 ER - TY - BOOK TI - Fuzzy differential equations in modeling hydraulic differential servo cylinders AU - A. Bencsik AU - B. Bede AU - J. Tar AU - J. Fodor PB - Third Romanian-Hungarian joint symposium on applied computational intelligence (SACI), Timisoara PY - 2006 DA - 2006// CY - Romania ID - Bencsik2006 ER - TY - JOUR TI - Fuzzy differential equations AU - J. J. Buckley AU - T. Feuring JO - Fuzzy Sets and Systems PY - 2000 DA - 2000// VL - 110 ID - Buckley2000 ER - TY - JOUR TI - Averaging fuzzy biopolymers AU - J. Casasnovas AU - F. Rosselló JO - Fuzzy Sets and Systems PY - 2005 DA - 2005// VL - 152 ID - Casasnovas2005 ER - TY - JOUR TI - Some properties of graded mean integration representation of L-R type fuzzy numbers AU - S. H. Chen AU - S. T. Wang AU - S. M. Chang JO - Tamsui Oxf. J. Math. Sci. PY - 2006 DA - 2006// VL - 22 ID - Chen2006 ER - TY - JOUR TI - A fuzzy Cauchy problem modelling the decay of the biochemical oxygen demand in water AU - G. L. Diniz AU - J. F. R. Fernandes AU - J. F. C. A. Meyer AU - L. C. Barros JO - Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver, BC, Canada PY - 2001 DA - 2001// VL - 1 ID - Diniz2001 ER - TY - JOUR TI - From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold AU - M. S. El Naschie JO - Chaos Solitons Fractals PY - 2005 DA - 2005// VL - 25 ID - Naschie2005 ER - TY - JOUR TI - An iterative scheme for the solution of generalized system of linear fuzzy differential equations AU - O. S. Fard JO - World Appl. Sci. J. PY - 2009 DA - 2009// VL - 7 ID - Fard2009 ER - TY - JOUR TI - A geometric approach to solve fuzzy linear systems of differential equations AU - N. Gasilov AU - Ş. E. Amrahov AU - A. G. Fatullayev JO - Appl. Math. Inf. Sci. PY - 2011 DA - 2011// VL - 5 ID - Gasilov2011 ER - TY - JOUR TI - Several sequential augmentations of Richardson’s arms race model AU - W. W. Hill JO - Math. Comput. Model. PY - 1992 DA - 1992// VL - 16 ID - Hill1992 ER - TY - JOUR TI - An approach to modelling and simulation of uncertain dynamical systems AU - E. Hüllermeier JO - Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, Fuzziness Knowledge-Based Systems PY - 1997 DA - 1997// VL - 5 ID - Hüllermeier1997 ER - TY - BOOK TI - Numerical solution of system of fractional differential equations in imprecise environment AU - N. A. Khan AU - O. A. Razzaq AU - A. Ara AU - F. Riaz PB - Numerical Simulation-From Brain Imaging to Turbulent Flow PY - 2016 DA - 2016// CY - InTech ID - Khan2016 ER - TY - JOUR TI - On the solution of fuzzy differential equations by Fuzzy Sumudu Transform AU - N. A. Khan AU - O. A. Razzaq AU - M. Ayyaz JO - Nonlinear Eng. PY - 2015 DA - 2015// VL - 4 ID - Khan2015 ER - TY - JOUR TI - A new fuzzy approximation method to Cauchy problems by fuzzy transform AU - A. Khastan AU - I. Perfilieva AU - Z. Alijani JO - Fuzzy Sets and Systems PY - 2016 DA - 2016// VL - 288 ID - Khastan2016 ER - TY - JOUR TI - An introduction to mathematical models in the social and life sciences AU - M. J. McLean JO - M. Olinick Addison-Wesley Inc., London, (1978), Appl. Math. Modell. PY - 1979 DA - 1979// VL - 3 ID - McLean1979 ER - TY - JOUR TI - Fuzzy differential equations and the extension principle AU - M. T. Mizukoshi AU - L. C. Barros AU - Y. Chalco-Cano AU - H. Román-Flores AU - R. C. Bassanezi JO - Inform. Sci. PY - 2007 DA - 2007// VL - 177 ID - Mizukoshi2007 ER - TY - JOUR TI - First order linear non homogeneous ordinary differential equation in fuzzy environment AU - S. P. Mondal AU - T. K. Roy JO - Math. Theory Model. PY - 2013 DA - 2013// VL - 3 ID - Mondal2013 ER - TY - JOUR TI - Effect of different defuzzification methods in a fuzzy based load balancing application AU - S. Naaz AU - A. Alam AU - R. Biswas JO - Int. J. Comput. Sci. PY - 2011 DA - 2011// VL - 8 ID - Naaz2011 ER - TY - JOUR TI - Another method for defuzzification based on regular weighted point AU - R. Saneifard JO - Int. J. Ind. Math. PY - 2011 DA - 2011// VL - 4 ID - Saneifard2011 ER - TY - JOUR TI - A method for defuzzification based on centroid point AU - R. Saneifard AU - R. Saneifard JO - Turkish J. Fuzzy Sys. PY - 2011 DA - 2011// VL - 2 ID - Saneifard2011 ER - TY - JOUR TI - Fuzzy modeling and control of HIV infection AU - H. Zarei AU - A. V. Kamyad AU - A. A. Heydari JO - Comput. Math. Methods Med. PY - 2012 DA - 2012 // VL - 2012 ID - Zarei2012 ER - TY - JOUR TI - A dye removal model with a fuzzy initial condition AU - Y. Zhang AU - J.-H. He AU - S.-Q. Wang AU - P. Wang JO - Therm. Sci. PY - 2016 DA - 2016// VL - 20 ID - Zhang2016 ER -