基于扩展相容性关系的通用证据模型建立过程
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摘要
证据建模已经成为当前制约D—S证据理论广泛应用的一个瓶颈问题。Dempster(1967)基于在多值映射方面的工作,率先提出了相容性关系这一重要概念;Shafer(1976)根据这一概念,定义了信任函数(即证据模型)。本文通过扩展信任函数的相容性关系,探索性地描述了一个适用于各种不确定性的通用证据模型的建立过程。通用证据模型的建立过程与Appriou(1999)的证据模型1相比,物理意义更加明确,理论体系更加完整;与其他针对具体应用背景的证据建模方法相比,适用范围更加广泛。
Evidence modeling has become a bottleneck problem of restricting the application of D-S evidence theory currently. Dempster(1967) firstly brought forward an important concept-compatibility relation based on the research of multi-value mapping. Shafer(1985) defined basic probability assignment function-the model of evidence based on the compatibility relation later. By extending compatibility relation of belief function, the process of founding a generic evidential model is described for kinds of uncertainty in this paper. Compared with Appriou's(1999) first model, the physical meaning of the process of founding the generic evidential model is much more explicit and the system info is much more integrated. This process of modeling has wider range of application than other modeling methods of evidence.
Evidence modeling has become a bottleneck problem of restricting the application of D-S evidence theory currently. Dempster(1967) firstly brought forward an important concept-compatibility relation based on the research of multi-value mapping. Shafer(1985) defined basic probability assignment function-the model of evidence based on the compatibility relation later. By extending compatibility relation of belief function, the process of founding a generic evidential model is described for kinds of uncertainty in this paper. Compared with Appriou's(1999) first model, the physical meaning of the process of founding the generic evidential model is much more explicit and the system info is much more integrated. This process of modeling has wider range of application than other modeling methods of evidence.
引文
[1] Lawrence D S, Thomas L C, James B H. Technical documentation of nodestar(AD-A302458) . Naval Research Laboratory, Washington, DC, 1995．
[2] Shafer G A. Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press, 1976:35-56．
[3] Shafer G. Belief functions and possibility measures. Analysis of Fuzzy Information, edited by J.C. Bezdek, Boca Raton, Fla: CRC Press, 1985: 55-60．
[4] George J K. Uncertainty in the Dempster-Shafer theory: a critical re-examination. Int. J. ofGeneral Systems, 1990, 18(2) : 155-166．
[5] Smets P. The combination of evidence in the transferable belief modal. IEEE Trans, on Pattern Analysis and Machine Intelligence, 1990, 12(5) : 447-458．
[6] Ngwenyama O K, Bryson N. Generating belief functions from qualitative preferences: An approach to eliciting expert judgments and deriving probability functions. Data & Knowledge Engineering, 1998, 28(2) : 145-159．
[7] Coombs K,Freel D, et al. Using Dempster-Shafer methods for object classification in the theater ballistic missile environment, SPIE vol.3719, Sensor Fusion:Architectures, Algorithms and Applications III, 1999: 103-113．
[8] 罗志增,蒋挣坪.基于D-S理论的多信息融合方法及应用.电子学报,1999,27(9) :100-102．
[9] Appriou A. Multisensor signal processing in the framework of the theory of evidence.NATO/RTO-Lecture Series 216 on Application of Mathematical Signal Processing Techniquesto Mission Systems, 1999．
[10] Lingras P, Wong S K M. Two perspectives of the Dempster-Shafer theory of belief functions. Int.J. Man-Machine Studies, 1990, 33(5) : 467-487．
[11] Dempster A P. Upper and lower probabilities induced by multivalued mapping. Ann. Math.Stat., 1967, 38(3) : 325-339．
[12] 曲大健.不确定性推理的证据理论方法在地震信号解释中的应用.[博士论文],北京:清华大学,1993．
[2] Shafer G A. Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press, 1976:35-56．
[3] Shafer G. Belief functions and possibility measures. Analysis of Fuzzy Information, edited by J.C. Bezdek, Boca Raton, Fla: CRC Press, 1985: 55-60．
[4] George J K. Uncertainty in the Dempster-Shafer theory: a critical re-examination. Int. J. ofGeneral Systems, 1990, 18(2) : 155-166．
[5] Smets P. The combination of evidence in the transferable belief modal. IEEE Trans, on Pattern Analysis and Machine Intelligence, 1990, 12(5) : 447-458．
[6] Ngwenyama O K, Bryson N. Generating belief functions from qualitative preferences: An approach to eliciting expert judgments and deriving probability functions. Data & Knowledge Engineering, 1998, 28(2) : 145-159．
[7] Coombs K,Freel D, et al. Using Dempster-Shafer methods for object classification in the theater ballistic missile environment, SPIE vol.3719, Sensor Fusion:Architectures, Algorithms and Applications III, 1999: 103-113．
[8] 罗志增,蒋挣坪.基于D-S理论的多信息融合方法及应用.电子学报,1999,27(9) :100-102．
[9] Appriou A. Multisensor signal processing in the framework of the theory of evidence.NATO/RTO-Lecture Series 216 on Application of Mathematical Signal Processing Techniquesto Mission Systems, 1999．
[10] Lingras P, Wong S K M. Two perspectives of the Dempster-Shafer theory of belief functions. Int.J. Man-Machine Studies, 1990, 33(5) : 467-487．
[11] Dempster A P. Upper and lower probabilities induced by multivalued mapping. Ann. Math.Stat., 1967, 38(3) : 325-339．
[12] 曲大健.不确定性推理的证据理论方法在地震信号解释中的应用.[博士论文],北京:清华大学,1993．
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