模糊微分的性质
|
摘要
在求解由刘过程驱动的模糊微分方程时,需要研究一类新的模糊微分(刘微分)的性质.给出了模糊微分的2个中值定理和4个模糊微分公式,并且将这些结论推广到复模糊微分的情形.这些工作为模糊微分方程理论的完善和应用奠定了基础.
To solve fuzzy differential equation driven by Liu process,some properties of a new kind of fuzzy differential(Liu differential)are needed.Two mean value theorems of fuzzy differential and four fuzzy differential formulas are given in this paper.Furthermore,these conclusions are extended to the case of complex fuzzy process.The studies above lay a theoretical foundation for calculation and application of the fuzzy differential equation.
To solve fuzzy differential equation driven by Liu process,some properties of a new kind of fuzzy differential(Liu differential)are needed.Two mean value theorems of fuzzy differential and four fuzzy differential formulas are given in this paper.Furthermore,these conclusions are extended to the case of complex fuzzy process.The studies above lay a theoretical foundation for calculation and application of the fuzzy differential equation.
引文
[1]ZADEH L A.Fuzzy sets as a basis for a theory of possibility[J].Fuzzy Sets and Systems,1987,1(1):3-28.
[2]ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[3]NAHMIAS S.Fuzzy variables[J].Fuzzy Sets and Systems,1987,1(2):97-110.
[4]YAGER R.A foundation for a theory of possibility[J].Journal of Cybernetics,1980,10(1-3):177-204.
[5]COOMAN De G.Possibility theory I-III[J].International Journal of General Systems,1997,25(4):291-371.
[6]DUBOIS D,PRADE H.Possibility theory:an approach to computerized processing of uncertainty[M].New York:Plenum,1988.
[7]LIU Baoding,LIU Yankui.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transaction on Fuzzy Systems,2002,10(4):445-450.
[8]LI Xiang,LIU Baoding.Chance measure for hybrid events with fuzziness and randomness[J].Soft Computing,2009,13(2):105-115.
[9]LIU Baoding.Uncertainty theory:an introduction to its axiomatic foundations[M].Berlin:Springer-verlag,2004.
[10]LIU Baoding.Fuzzy process,hybrid process and uncertain process[J].Journal of Uncertain Systems,2008,2(1):3-16.
[11]YOU Cuilian,HUO Huae,WANG Weiqing.Multi-dimensional Liu process,differential and integral[J].Journal of East Asian Mathematical,2013,29(1):13-22.
[12]QIN Zhongfeng.On analytic function of complex Liu process.[EB/OL].(2008-04-12)[2013-10-02].http://orsc.edu.cn/process/071026.pdf,2007.
[13]尤翠莲,王根森.一类新的模糊积分的性质[J].河北大学学报:自然科学出版社,2011,31(4):337-340.YOU Cuilian,WANG Gensen.Properties of a new kind of fuzzy integral[J].Journal of Hebei University:Natural Science Edition,2011,31(4):337-340.
[14]ZHU Yuanguo.Fuzzy control theory[EB/OL].(2008-07-05)[2013-10-02].http://orsc.edu.cn/~yhzhu/fct.pdf.
[15]ZHU Yuanguo.Fuzzy optimal control with application to portfolio selection[EB/OL].(2008-01-17)[2013-10-02].http://orsc.edu.cn/process/080117.pdf.
[16]LIU Linzhong,LI Yinzhen.The fuzzy quadratic assignment problem with penality:new models and genetic algorithm[J].Applied Mathematics and Computation,2006,174(2):1229-1224.
[17]LIU Yankui,LIU Baoding.Random fuzzy programming with chance measures defined by fuzzy integrals[J].Mathematical and Computer Modelling,2002,36(4-5):509-524.
[18]LIU Baoding,LIU Yankui.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transactions on Fuzzy Systems,2002,10(4):445-450.
[19]QIN Zhongfeng,LI Xiang.Option pricing formula for fuzzy financial market[J].Journal of Uncertain Systems,2008,2(1):17-21.
[2]ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[3]NAHMIAS S.Fuzzy variables[J].Fuzzy Sets and Systems,1987,1(2):97-110.
[4]YAGER R.A foundation for a theory of possibility[J].Journal of Cybernetics,1980,10(1-3):177-204.
[5]COOMAN De G.Possibility theory I-III[J].International Journal of General Systems,1997,25(4):291-371.
[6]DUBOIS D,PRADE H.Possibility theory:an approach to computerized processing of uncertainty[M].New York:Plenum,1988.
[7]LIU Baoding,LIU Yankui.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transaction on Fuzzy Systems,2002,10(4):445-450.
[8]LI Xiang,LIU Baoding.Chance measure for hybrid events with fuzziness and randomness[J].Soft Computing,2009,13(2):105-115.
[9]LIU Baoding.Uncertainty theory:an introduction to its axiomatic foundations[M].Berlin:Springer-verlag,2004.
[10]LIU Baoding.Fuzzy process,hybrid process and uncertain process[J].Journal of Uncertain Systems,2008,2(1):3-16.
[11]YOU Cuilian,HUO Huae,WANG Weiqing.Multi-dimensional Liu process,differential and integral[J].Journal of East Asian Mathematical,2013,29(1):13-22.
[12]QIN Zhongfeng.On analytic function of complex Liu process.[EB/OL].(2008-04-12)[2013-10-02].http://orsc.edu.cn/process/071026.pdf,2007.
[13]尤翠莲,王根森.一类新的模糊积分的性质[J].河北大学学报:自然科学出版社,2011,31(4):337-340.YOU Cuilian,WANG Gensen.Properties of a new kind of fuzzy integral[J].Journal of Hebei University:Natural Science Edition,2011,31(4):337-340.
[14]ZHU Yuanguo.Fuzzy control theory[EB/OL].(2008-07-05)[2013-10-02].http://orsc.edu.cn/~yhzhu/fct.pdf.
[15]ZHU Yuanguo.Fuzzy optimal control with application to portfolio selection[EB/OL].(2008-01-17)[2013-10-02].http://orsc.edu.cn/process/080117.pdf.
[16]LIU Linzhong,LI Yinzhen.The fuzzy quadratic assignment problem with penality:new models and genetic algorithm[J].Applied Mathematics and Computation,2006,174(2):1229-1224.
[17]LIU Yankui,LIU Baoding.Random fuzzy programming with chance measures defined by fuzzy integrals[J].Mathematical and Computer Modelling,2002,36(4-5):509-524.
[18]LIU Baoding,LIU Yankui.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transactions on Fuzzy Systems,2002,10(4):445-450.
[19]QIN Zhongfeng,LI Xiang.Option pricing formula for fuzzy financial market[J].Journal of Uncertain Systems,2008,2(1):17-21.