A new method to find fuzzy nth order derivation and applications to fuzzy nth order arithmetic based on generalized h-derivation

A new method to find fuzzy nth order derivation and applications to fuzzy nth order arithmetic based on generalized h-derivation

In this paper, fuzzy nth-order derivative for n ? N is introduced. To do this, nth-orderderivation under generalized Hukuhara derivative here in discussed. Calculations on the fuzzy nthorder derivative on fuzzy functions and their relationships, in general, are introduced. Then, the fuzzynth-order differential equations is solved, for n ? N

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  • [1] Allahviranloo, T., Ahmady, E., Ahmady, N., A method for solving nth order fuzzy linear differential equations, International Journal of Computer Mathematics, 86, 730-742 (2009).
  • [2] Allahviranloo, T., Ahmady, E., Ahmady, N., Nthorder fuzzy linear differential equations, Information sciences, 178, 1309-1324 (2008).
  • [3] Allahviranloo, T., Ahmady, E., Ahmady, N., Numerical solution of fuzzy differential equations by predictor-corrector method, Information sciences, 177, 1633-1647 (2007).
  • [4] Allahviranloo, T., Hooshangian, L., Fuzzy generalized H-differential and applications to fuzzy differential equations of second-order, Journal of Intelligent and Fuzzy Systems, In press.
  • [5] Allahviranloo, T., Kiani, N., Barkhordari, N., Toward the existence and uniqueness of solution of second order fuzzy differential equations, Information sciences, 179, 1207-1215 (2009).
  • [6] Bede, B., Note on "Numerical solution of fuzzy differential equations by predictor-corrector method, Information sciences, 178, 1917-1922, (2008).
  • [7] Bede, B., Rudas, I.J., Bencsik, A.L., First order linear fuzzy differential equations under generalizes differentiability, Information Sciences, 177, 1648-1662, (2007).
  • [8] Bede, B., Gal, S.G., Generalizations of differentiability of fuzzy number value function with applications to fuzzy differential equations, Fuzzy sets and systems, 151, 581-599 (2005).
  • [9] Buckley, J., Feuring, T., Jimenez-Gamero, M.D., Fuzzy differential equation, Fuzzy Sets and Systems, 110, 43-54 (2000).
  • [10] Chalco-Cano, Y ., Roman-Flores, H., Fuzzy differential equations with generalized derivative, 27th ANFIPS International Conference IEEE, 1016-1043 (2008).
  • [11] Chalco-Cano, Y., Roman-Flores, H., On new solutions of fuzzy differential equations, Chaos Solitons and Fractals, 38, 112-119 (2008).
  • [12] Chalco-Cano, Y., Roman-Flores, H., JimenezGamero, M.D., Generalized derivative and ?-derivative for set-valued functions, Information Science, 181, 2177-2188 (2011).
  • [13] Diamond, P., Brief note on the variation of constance formula for fuzzy differential equations, Fuzzy Sets and Systems, 129, 65-71 (2002).
  • [14] Dubois, D., Prade, H., Theory and application, fuzzy sets and systems, Academic Press, (1980).
  • [15] Kaleva, O., A note on fuzzy differential equations, Nonlinear Analysis, 64, 895-900 (2006).
  • [16] Kaleva, O., Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987).
  • [17] Kauffman, A., Gupta, M.M., Introduction to Fuzzy Arithmetic: Theory and Application, Van Nostrand Reinhold, New York, (1991).
  • [18] Khastan, A., Nieto, J.J., A boundary value problem for second order fuzzy differential equations, Nonlinear analysis, 72, 3583-3593 (2010).
  • [19] Nieto, J.J., Lopez, R.R., Fuzzy differential system under generalized metric space approach, Dynamic System Application, 17, 1342-1357 (2008).
  • [20] Puri, M., Ralescu, D., Differential and fuzzy functions, Mathematics Analysis and Applications, 91, 552-558 (1983).
  • [21] Salahshour, S., Nth order fuzzy differential equations under generalized differentiability, Fuzzy sets valued analysis systems, (2011).
  • [22] Siekalla, S., On the fuzzy initial value problem, Fuzzy sets and systems, 24, 319-330 (1987).
  • [23] Stefanini, L., A generalization of Hukuhara difference and division for interval and fuzzy arithmetics, Fuzzy Sets and Systems, 161, 1564-1584 (2010).
  • [24] Stefanini, L., Bede, B., Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis, 71, 1311- 1328 (2009).
  • [25] Zadeh, L.A., Fuzzy Sets, Information and Control, 8, 338-353 (1965).
  • [26] Zhang, D., Feng, W., Zhao, Y., Qiu, J., Global existence of solutions for fuzzy second order differential equations under generalize H-differentiability, Computers and Mathematics with Applications, 60, 1548- 1556 (2010).
  • [27] Zimmermann, H.J., Fuzzy sets theory and its applications, Kluwer Academic Press, Dordrecht, (1991)