基于泰勒展开式的模糊微分方程数值解法

doi:10.3969/j.issn.1000-1565.2018.02.001

河北大学学报(自然科学版) ›› 2018, Vol. 38 ›› Issue (2): 113-118.DOI: 10.3969/j.issn.1000-1565.2018.02.001

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基于泰勒展开式的模糊微分方程数值解法

尤翠莲,郝杨阳

收稿日期:2017-10-27 出版日期:2018-03-25 发布日期:2018-03-25
作者简介:尤翠莲(1977—),女,河北唐山人,河北大学副教授,博士,主要从事不确定理论与模糊微分方程的研究. E-mail:yycclian@163.com
基金资助:
国家自然科学基金资助项目(61374184)

Numerical method for solving fuzzy differential equations based on Taylor expansion

YOU Cuilian, HAO Yangyang

College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2017-10-27 Online:2018-03-25 Published:2018-03-25

摘要/Abstract

摘要： 由刘过程驱动的模糊微分方程是处理模糊动态问题的重要工具,在求解由刘过程驱动的模糊微分方程时,有一些模糊微分方程并不能求出其解析解,这时往往需要研究一些可以求出模糊微分方程近似解的方法.本文利用模糊Taylor展开式,给出了一种基于模糊Taylor展开式的模糊微分方程数值解法,并证明了该数值解法的收敛性.

关键词: 刘过程, 模糊微分, 模糊积分, 模糊微分方程, Taylor公式

Abstract: Fuzzy differential equation driven by Liu process is an important tool to deal with dynamic fuzzy problem. When solving fuzzy differential equation,the analytical solution for some fuzzy differential equation driven by Liu process can’t be obtained sometimes,thus it is necessary for us to discuss the numerical method in most situations.In this paper,a numerical method for solving fuzzy differential equation based on fuzzy Taylor expansion is given and its convergence is also proved.

Key words: Liu process, fuzzy differential, fuzzy integral, fuzzy differential equation, Taylor expansion

中图分类号:

O159

尤翠莲,郝杨阳. 基于泰勒展开式的模糊微分方程数值解法[J]. 河北大学学报(自然科学版), 2018, 38(2): 113-118.

YOU Cuilian, HAO Yangyang. Numerical method for solving fuzzy differential equations based on Taylor expansion[J]. Journal of Hebei University (Natural Science Edition), 2018, 38(2): 113-118.

参考文献

[1] ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.DOI:10.1016/S0019-9958(65)90241-X.
[2] ZADEH L A.Fuzzy sets as a basis for a theory of possibility[J].Fuzzy Sets and Systems,1978,1(1):3-28.DOI:10.1016/0165-0114(78)90029-5.
[3] LIU B D,LIU Y K.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transactions on Fuzzy Systems,2002,10(4):445-450.DOI:10.1109/TFUZZ.2002.800692.
[4] LI X,LIU B D.A sufficient and necessary condition for credibility measures[J].International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2006,14(5):527-535.DOI:10.1142/S0218488506004175.
[5] LIU B D.Uncertainty Theory[M].Springer-Verlag,Berlin,2004.
[6] LIU B D.Uncertainty Theory[M].2nd ed.Berlin,Springer-Verlag,2007.
[7] LIU B D.Fuzzy process,hybrid process and uncertain process[J].Journal of Uncertain Systems,2008,2(1):3-16.
[8] DAI W.Lipschitz continuity of Liu process.[EB/OL].(2008-08-31)[2016-08-02].http://orsc.edu.cn/ proc ess/080831.pdf.
[9] DAI W.Reflection principle of Liu process[J].[EB/OL].(2008-07-05)[2016-08-02].http://orsc.edu.cn/process/071110.pdf.
[10] QIN Z F,WEN M L.On analytic functions of complex Liu process[J].Journal of Intelligent and Fuzzy Systems,2015,28(4):1627-1633.DOI:10.3233/IFS-141448.
[11] GAO J W,GAO X.A new stock model for credibilistic option pricing[J].Journal of Uncertain Systems,2008,4(2):243-247.
[12] 尤翠莲,王根森.一类新的模糊积分的性质[J].河北大学学报(自然科学版),2011,31(4):337-340.DOI:10.3969/j.issn.1000-1565.2011.04.001. YOU C L, WANG G S.Properties of a new kind of fuzzy integral[J].Journal of Hebei University(Natural Science Edition),2011,31(4):337-340.DOI:10.3969/j.issn.1000-1565.2011.04.001.
[13] 尤翠莲,王伟卿.模糊微分的性质[J].河北大学学报(自然科学版),2015,35(2):113-116.DOI:10.3969/j.issn.1000-1565.2015.02.001. YOU C L, WANG W Q.Properties of fuzzy differential[J].Journal of Hebei University(Natural Science Edition),2015,35(2):113-116.DOI:10.3969/j.issn.1000-1565.2015.02.001.
[14] YOU C L,HUO H E,WANG W Q.Multi-dimensional Liu process,differential and integral[J].East Asian Mathematical Journal,2013,29(1):13-22.DOI:10.7858/eamj.2013.002.
[15] YOU C L,MA H Y,HUO H E.A new kind of generalized fuzzy integrals[J].Journal of Nonlinear Science and Applications,2016,3(9):1396-1402.DOI:10.22436/jnsa.009.03.63.
[16] LIU B D.Inequalities and convergence concepts of fuzzy and rough variables[J].Fuzzy Optimization and Decision Marking,2003,2(2):87-100.DOI:10.1023/A:1023491000011.
[17] LIU Y K,LIU B D.Random fuzzy programming with chance measures defined by fuzzy integrals[J].Mathematical and Computer Modelling,2002,36(4-5):509-524.DOI:10.1016/S0895-7177(02)00180-2.
[18] QIN Z F,LI X.Option pricing formula for fuzzy financial market[J].Journal of Uncertain Systems,2008,2(1):17-21.
[19] YOU C L,WANG W Q,HUO H E.Existence and uniqueness theorems for fuzzy differential equations[J].Journal of Uncertain Systems,2013,7(4):303-315.
[20] CHEN X W,QIN Z F.A new existence and uniqueness theorem for fuzzy differential equation[J].International Journal of Fuzzy Systems,2011,13(2):148-151.
[21] ZHU Y G.Stability analysis of fuzzy linear differential equations[J].Fuzzy Optimization and Decision Making,2010,9(2):169-186.DOI:10.1007/s10700-010-9080-3.
[22] ZHU Y G.A fuzzy optimal control model[J].Journal of Uncertain Systems,2009,3(4):270-279.
[23] QIN Z F,BAI M Y,RALESCU D A.A fuzzy control system with application to production planning problems[J].Information Sciences,2011,181(5):1018-1027.DOI:10.1016/j.ins.2010.10.029.
[24] HAO Y Y,YOU C L.Multi-dimensional fuzzy Euler approximation[J].Mathematica Aeterna,2017,2(7):163-176.

基于泰勒展开式的模糊微分方程数值解法

Numerical method for solving fuzzy differential equations based on Taylor expansion

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