Modeling, Reasoning And Learning Approach To Evidential Network

Uncertainty decision making is a very important research field in management science and applications. The real-world probems often involve many components and elements, which are interrelated and interactional. At the same time, large numbers of uncertainty exact among these elements and their relation. The uncertainty includes alearoty and epistemic uncertainty. The former is referred to as variability, irreducible and stochastic uncertainty. The later is also refered to as reducible, subjective and state-of-knowledge uncertainty, which is due to lack of knowledge or ambiguity. So, the new challenges in uncertainty management and decision research are how to describe various types of uncertainties, how to analyze and model complex relation of system, and how to aggregate quantitative data and qualitative knowledge for making correct decision.In order to meet the above challenges, the Evidential Network model is proposed, which follows the methodology of qualitative and quantitative information integration and research road of Bayesian network, on the basis of Dempster-Shafer theory of evidence and graph theory. The Evidential Network is a combination of and graph model. It has the capability, which comes from D-S theory, to deal uncertain information, especially the epistemic uncertainty. It also has advantages of discirbing problems and analyzing relationship, which comes from graph theory. In theoretical prospect, the Evidential Network will develop research ideas and methods for modeling and analyzing uncertainty, and develop technology and tools which build a uniform treatment framework for aggregating quantitative data and qualitative knowledge. In application prospect, it will provide technology and methods for analyzing, modeling, inference, assessment, and decision making in uncertainty management problems.For completing the theorerical and technical framework of Evidential Network model, this paper focuses on the research works of definition, topology constructing, parameter formulation, reasoning under different parameter models, and parameter learning as follows.Firstly, the basic concept of Evidential Network is defined, including elements, characteristics, and modeling process. The Evidential Network can describe the relations among variables using the directed acyclic graph under qualitative views, and denote the influence modes and degree under qualitative views. It has the advantages of D-S theory and graph theory, and provides a technical tool for describing uncertainty, modeling relations, and dealinig with information. The construction methods based on tree model and causal network are proposed for constructing the topology of Evidential Network. The parameter models of Evidential Network are formulated with knowledge description under framework of D-S theory, which consiste of two types: Conditional Belief Function (CBF) and Belief Rule Model (BRM).Secondly, the Evidential Network reasoning frameworks and approach with CBF and BRM parameter model are respectively analyzed. The forward causal and backward diagnosis reasoning for Evidential Network with CBF are solved using conditional belief inference and computing algorithms. A new belief combination algorithm is proposed based on a new belief conflict measurement, which avoids the conflict paradox of Dempster combination rule, to combine nodes'information of Evidential Network. In Evidential Network reasoning with BRM, a weight generating method based on goal programming is proposed to obtain EN nodes'priority under incomplete information environment. The EN reasoning with BRM is accomplished following several steps: belief structure data transformation, action weights of belief rule, evidetnaitl reasoning algorithms, and belief structure result analysis.Then, the mathematic formulations for EN parameters learning is constructed, and learning algorithms are proposed based on Rosen projection grads method. For Evidential Network with BRM, the parameters learning problem is transformed to an nonlinear objective optimization problems. The objective function of optimization problems is constructed by using a belief structure distance measurement, which defines the difference between belief structure models and has some basic property of distance measurement. The grads of objective function needs to be gotten when the projection grads method is used to solve optimation problems. The whole solution process is proposed steps by steps for EN parameters learning from historical data or experience knowledge.Finally, the solution process and approaches to Evidential Network, which are proposed in this paper, are used to deal with safety analysis and evaluation of aerospace system, military threat assessment and prediction, and risk forecasting of traffic accidents. These applications are examined to illustrate and show the feasibility and validity of the Evidential Network model, and to indicate the research and application value in the future system analysis, management, and uncertainty decision.