结构元理论下的模糊Markov决策过程Fuzzy Markov decision process based on structural element theory
任思行;郭嗣琮;曾繁慧;
摘要(Abstract)：
为解决模糊Markov决策过程中λ-截集计算的复杂性问题,利用模糊结构元理论建模及求解.对于状态模糊情况,分别给出全部状态模糊与部分状态模糊的模糊Markov过程定义,模糊结构元建模及优化决策;给出具有模糊转移矩阵的Markov过程定义,结构元建模及优化决策;给出状态及转移矩阵均模糊的Markov过程定义,结构元建模及优化决策.实例分析结果表明:模糊Markov过程的结构元建模及优化决策是简单有效的.
关键词(KeyWords)： 模糊结构元;模糊Markov;模糊状态;模糊转移矩阵;结构元加权排序
基金项目(Foundation): 辽宁省教育厅科学经费项目（LJ2019JL019）
作者(Authors): 任思行;郭嗣琮;曾繁慧;
参考文献(References)：
- [1] ALAGOZ O,HSU H,SCHAEFER A J,et al.Markov decision processes:a tool for sequential decision making under uncertainty[J].Medical Decision Making,2010,30(4):474-483.
- [2] SYMEONAKI M A,STAMOU G B.Theory of Markov systems with fuzzy states[J].Fuzzy Sets and Systems,2004(143):427-445.
- [3] SYMEONAKI M A,STAMOU G B.Rate of convergence,asymptotically attainable structures and sensitivity in non-homogeneous Markov systems with fuzzy states[J].Fuzzy Sets and Systems,2006(157):143-159.
- [4] KURANO M,YASUDA M,NAKAGAMI J,et al.A fuzzy approach to Markov decision processes with uncertain transition probabilities[J].Fuzzy Sets and Systems,2006(157):2 674-2 682.
- [5] VASSILIOU P C G.Fuzzy semi-Markov migration process in credit risk[J].Fuzzy Sets and Systems,2013(223):39-58.
- [6]郭嗣琮.模糊分析中的结构元方法(Ⅰ)、(Ⅱ)[J].辽宁工程技术大学学报,2002,21(5):670-673,21(6):808-810.GUO Sicong.Method of structuring element in fuzzy analysis(Ⅰ)、(Ⅱ)[J].Journal of Liaoning Technical University(Natural Science),2002,21(5):670-673,21(6):808-810.
- [7]郭嗣琮.基于结构元理论的模糊数学分析原理[M].沈阳:东北大学出版社,2004.
- [8]王磊,郭嗣琮.线性生成的完全模糊线性微分系统[J].系统工程理论与实践,2012,32(2):341-348.WANG Lie,GUO Sicong.Linear formed fully fuzzy linear differential systems[J].Systems Engineering Theory&Practice,2012,32(2):341-348.
- [9]杨纶标,高英仪,凌卫新.模糊数学原理及应用(第5版)[M].广州:华南理工大学出版社, 2011.
- [10] MALAY B.Fuzzy Markovian decision process[J].Fuzzy Sets and Systems,1998,99(3):273-282