基于大焦元的子焦元的信任函数逼近方法
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摘要
对于证据合成过程中焦元数目过多导致计算量较大的问题,该文给出了一种综合考虑焦元的基数大小和信任值大小的信任函数逼近方法,该方法可以控制焦元数目、加快运算速度,通过算例分析验证了结论的有效性.
For the problem that the number of focal elements is too much in the process of evidence synthesis so as to have large computational complexity,a belief function approximation method considering the size of the cardinal number and the belief value of focal elements is presented. This method can control the number of focal elements and speed up the calculation. The validity of the conclusion is verified by the analysis of examples.
For the problem that the number of focal elements is too much in the process of evidence synthesis so as to have large computational complexity,a belief function approximation method considering the size of the cardinal number and the belief value of focal elements is presented. This method can control the number of focal elements and speed up the calculation. The validity of the conclusion is verified by the analysis of examples.
引文
[1]Shafer G.A mathematical theory of evidence[M].Princeton:Princeton University Press,1976.
[2]Dubois D,Prade H.Consonant approximations of belief functions[J].International Journal of Approximate Reasoning,1990,4(5):419-449.
[3]Bauer M.Approximation algorithms and decision making in the Dempster-Shafer theory of evidence:an empirical study[J].International Journal of Approximate Reasoning,1997,17(2):217-237.
[4]Bauer M.Approximations for decision making in the Dempster-Shafer theory of evidence[C]//In Proceedings of the Twelfth International Conference on Uncertainty in Artificial Intelligence.San Francisco:Morgan Kaufmann Publishers,1996:73-80.
[5]Tessem B.Approximations for efficient computation in the theory of evidence[J].Artificial Intelligence,1993,61(2):315-329.
[6]Lowrance J D,Garvey T D,Strat T M.A framework for evidential-reasoning systems[C]//Proceedings of the Fifth National Conference on Artificial Intelligence,Haarlem:Elsevier-North Holland Publishers,1986:896-903.
[7]Smets P.Belief functions versus probability functions[M]//Saitta L,Bouchon B,Yager R,ed.Berlin:SpringerVerlag,1988:17-24.
[8]Smets P.Decision making in the TBM:the necessity of the pignistic transformation[J].Approximate Reasoning,2005,38(2):133-147.
[9]Cobb B R,Shenoy P P.On transforming belief function models to probability models[R].Working Paper 293,University of Kansas School of Business,2003.
[10]Cobb B R,Shenoy P P.A comparison of Bayesian and belief function reasoning[J].Information Systems Frontiers,2003,5(4):345-358.
[11]Cobb B R,Shenoy P P.A comparison of methods for transforming belief function models to probability models[J].Lecture Notes in Computer Science,2003,2711:255-266.
[12]Cuzzolin F.Two new Bayesian approximations of belief functions based on convex geometry[J].Transactions on Systems,Man,and Cybernetics(B):Cybernetics,2007,37(4):993-1008.
[13]Cuzzolin F.Lp consonant approximations of belief functions[J].Transactions on Fuzzy Systems,2014,22(2):420-436.
[14]程子成,吴根秀,宋姝婷.基于融合信息熵性质的信任函数概率逼近[J].江西师范大学学报:自然科学版,2014,38(5):534-538.
[15]黄梅,吴根秀,刘邱云,等.一种基于大焦元分解的信任函数逼近方法[J].江西师范大学学报:自然科学版,2016,40(3):285-289.
[16]Harmanec D.Faithful approximations of belief functions[C]//UAI'99 Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence,San Francisco:Morgan Kaufmann Publishers,1999:271-278.
[17]Voorbraak F.A computationally efficient approximation of Dempster-Shafer theory[J].International Journal of ManMachine Studies,1989,30(5):525-536.
[18]Sarabi-Jamab A,Araabi B N.Information-based evaluation of approximation methods in Dempster-Shafer theory[J].International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2016,24(4):503-535.
[2]Dubois D,Prade H.Consonant approximations of belief functions[J].International Journal of Approximate Reasoning,1990,4(5):419-449.
[3]Bauer M.Approximation algorithms and decision making in the Dempster-Shafer theory of evidence:an empirical study[J].International Journal of Approximate Reasoning,1997,17(2):217-237.
[4]Bauer M.Approximations for decision making in the Dempster-Shafer theory of evidence[C]//In Proceedings of the Twelfth International Conference on Uncertainty in Artificial Intelligence.San Francisco:Morgan Kaufmann Publishers,1996:73-80.
[5]Tessem B.Approximations for efficient computation in the theory of evidence[J].Artificial Intelligence,1993,61(2):315-329.
[6]Lowrance J D,Garvey T D,Strat T M.A framework for evidential-reasoning systems[C]//Proceedings of the Fifth National Conference on Artificial Intelligence,Haarlem:Elsevier-North Holland Publishers,1986:896-903.
[7]Smets P.Belief functions versus probability functions[M]//Saitta L,Bouchon B,Yager R,ed.Berlin:SpringerVerlag,1988:17-24.
[8]Smets P.Decision making in the TBM:the necessity of the pignistic transformation[J].Approximate Reasoning,2005,38(2):133-147.
[9]Cobb B R,Shenoy P P.On transforming belief function models to probability models[R].Working Paper 293,University of Kansas School of Business,2003.
[10]Cobb B R,Shenoy P P.A comparison of Bayesian and belief function reasoning[J].Information Systems Frontiers,2003,5(4):345-358.
[11]Cobb B R,Shenoy P P.A comparison of methods for transforming belief function models to probability models[J].Lecture Notes in Computer Science,2003,2711:255-266.
[12]Cuzzolin F.Two new Bayesian approximations of belief functions based on convex geometry[J].Transactions on Systems,Man,and Cybernetics(B):Cybernetics,2007,37(4):993-1008.
[13]Cuzzolin F.Lp consonant approximations of belief functions[J].Transactions on Fuzzy Systems,2014,22(2):420-436.
[14]程子成,吴根秀,宋姝婷.基于融合信息熵性质的信任函数概率逼近[J].江西师范大学学报:自然科学版,2014,38(5):534-538.
[15]黄梅,吴根秀,刘邱云,等.一种基于大焦元分解的信任函数逼近方法[J].江西师范大学学报:自然科学版,2016,40(3):285-289.
[16]Harmanec D.Faithful approximations of belief functions[C]//UAI'99 Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence,San Francisco:Morgan Kaufmann Publishers,1999:271-278.
[17]Voorbraak F.A computationally efficient approximation of Dempster-Shafer theory[J].International Journal of ManMachine Studies,1989,30(5):525-536.
[18]Sarabi-Jamab A,Araabi B N.Information-based evaluation of approximation methods in Dempster-Shafer theory[J].International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2016,24(4):503-535.